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find the dimensions of the rectangle


WebFind the dimensions of a rectangle with perimeter 100 m whose area is as large as possible. If you know some Latin, the name of a shape usually explains a lot. As we already know the perimeter and length, we can rewrite the equation: You might need to use addition or division to solve, or you might need to factor a quadratic equation or use the quadratic formula to solve. d = (2 A / sin()); Given perimeter and angle: To learn how to find the width of a rectangle using the diagonal and the length, scroll down! 4. l. where d1 is the outer diameter, d2 is the inner diameter, and l is the length of the tube. The formulas for the perimeter P and the area A of the rectangle are used to write equations as follows: P = 2 * L + 2 * W. A = L * W. To determine the length and width of a rectangle, you need to: Know the area of the rectangle. P (perimeter) = 2L + 2W The answer is 1.176 times the longer side. View solution > Show that the rectangle of maximum area that can be inscribed in a circle is a square. WebThe formula for the perimeter of a rectangle is (width + height) x 2, as seen in the figure below: This is the equivalent of adding all four sides, since opposite sides are of equal length by definition. The USA is in the middle of the ranking, mainly because of the eccentricity of Alaska and Hawaii. solve equation (1) for W: Step 1: Enter the value of the area and perimeter of the rectangle in the respective input boxes. Preview / Show more . In that case, you would use the formula: perimeter = 2 length plus 2 width. 3. How to Calculate the Area of a Rectangle. So if the shape is above our shape of interest like square and rectangle we can say that: For the other two figures, we can state analogically: Many different rankings exist, evaluating the countries whether by their areas, populations, level of education, or Nobel prize winners. A = W * L (2) Maximum area of a rectangle whose perimeter is $100$. A dialogue box may appear asking you about encoding. Before we can find the dimensions of the rectangle, we need find w first. To get this answer, apply the formula diagonal = (P - 8 A). RewriteEngine On Solution: The properties of a rectangle can be used to calculate the area of a rectangle. To derive these answers, use the Pythagorean theorem. Let's solve this equation: WebThe dimensions of the rectangle which has the maximum area, are. The length of a rectangle field is twice its breadth. Our trained team of editors and researchers validate articles for accuracy and comprehensiveness. We have, Length = 4.5 m and Breadth = 1.6 m Drag a dimension shape to the shape you want to measure, and glue the ends of the dimension shape to the points you want to measure. Optimisation problem on area of rectangle. It has four sides that create four angles. Step 1: Enter the value of the area and perimeter of the rectangle in the respective input boxes. See Also: Find length width rectangle given perimeter Show details In the case of a square, the area will become side 2. To find this rectangle's area, you need to: Convert feet to inches. The main difference between square and rectangle is that the length and breadth are equal for square. The area of a rectangle is defined as the total space occupied by it and perimeter is defined as the total length of the boundary of the rectangle. Now insert the above equation into the equation for the area (A): The area equation is given as A = ab. Medium. Community Expert , Jul 28, 2016. The perfect snowman calculator uses math & science rules to help you design the snowman of your dreams! Did you know that you can construct the golden triangle using only a straightedge and compass? No manual conversion is necessary for length, width and area units, which can all be selected independently. There are many rectangular objects around us. Its definition is that it has all four sides of equal length; alternatively, the angle between two diagonals is right. Try entering a couple of parameters in the fields beside the text or keep reading to find out what are the possible diagonal of a rectangle formulas. 4. A = area, Hard. First, let's write down three basic equations for the area, perimeter] and circumcircle radius: With the above equations, we can now derive various diagonal of a rectangle formulas that are used by this diagonal of a rectangle calculator: Given length/width and area: The area equation is given as A = ab. Therefore, the length of the rectangle is x + 4 cm. if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[336,280],'analyzemath_com-medrectangle-4','ezslot_3',341,'0','0'])};__ez_fad_position('div-gpt-ad-analyzemath_com-medrectangle-4-0'); Formulation of Problem In the case of a square, the area will become side 2. 4. l. where d1 is the outer diameter, d2 is the inner diameter, and l is the length of the tube. To find the width of a rectangle, use the formula: area = length width. Point to Visio Extras, and then click Dimensioning-Architectural or Dimensioning-Engineering. WebConsidering the use of length and diameter mentioned above, the formula for calculating the volume of a tube is shown below: volume = . Remember, squaring a number means to multiply the number by itself. If you don't have the area, you can use the rectangle's perimeter instead. To find this rectangle's area, you need to: Convert feet to inches. Manage Settings Finding the maximum perimeter of a rectangle inside of an enclosed region. How to find the width and length of a rectangle given area and perimeter? WebSo, the area of the large rectangle is \(6\times \frac{1}{10}=\frac{6}{10}\), or 0.6 square units. The answer is 8. Check out our length converter or area converter to find out how to switch between different units (SI and d = P / (2 sin(/2) + 2 cos(/2)); and. Index of 1 is a perfect rectangle, 0 is an infinite number of infinitely small islands. Doors or window glass did a storm or a golf ball break your window pane? WebOnline calculator to calculate the dimensions (length and width) of a rectangle given the area A and perimeter P of the rectangle . Find the area, in square metres, of a rectangle whose length = 4.5 m and breadth = 1.6 m. Solution . To learn how to find the width of a rectangle using the diagonal and the length, scroll down! How to use our "Dimensions of a Rectangle Calculator"? WebHere's how: 1) Write an equation that relates 45cm2, w+4 and w. To do so, we know that the area of the rectangle, 45cm 2 can be found by multiplying w with w+4. Rectangle vs. other shapes. Try our calculators dedicated to squares, e.g., the square calculator. (You may need to consult other articles and resources for that information.). Our Collatz conjecture calculator will introduce you to one of the unsolved problem of mathematics! 16 in = 10 in + 2 W / - 10 in WebTrying to find the dimensions of a rectangle that would result in the max area. There are conditions under which this problem has a solution (see formulation of problem below). In that case, you would use the formula: perimeter = 2 length plus 2 width. Step 1: Enter the value of the area and perimeter of the rectangle in the respective input boxes. If you have the area A and width w, its length w is determined as h = A/w. and Width Given Area Width Given Perimeter Length Given Area Length Given Perimeter. Our. P - 2 L = 2 W This name derives from the fact that a rectangle is a quadrilateral with four right angles (4 90 = 360). If not, correct the error or revert back to the previous version until your site works again. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in). How do I find the area of a rectangle if width and perimeter are given? Step #3 - Find points of intersection. The area of a rectangle is a space restricted by its sides or, in other words, within the perimeter of a rectangle. WebThe formula for finding the area of a rectangle. Opposite sides of a rectangle are parallel to each other and have equal lengths. You divide the volume by the height and the length. WebCalculate a Rectangle Area Calculator Use. To find the width of a rectangle, use the formula: area = length width. If this doesn't work, you may need to edit your .htaccess file directly. Type the area and perimeter values into the calculator. WebFind the dimensions of a rectangle with perimeter 100 m whose area is as large as possible. WebSo, the area of the large rectangle is \(6\times \frac{1}{10}=\frac{6}{10}\), or 0.6 square units. Point to Visio Extras, and then click Dimensioning-Architectural or Dimensioning-Engineering. Level up your tech skills and stay ahead of the curve. Knowing your BMR (basal metabolic weight) may help you make important decisions about your diet and lifestyle. When you have a missing image on your site you may see a box on your page with with a red X where the image is missing. Check out 23 similar 2d geometry calculators , Harris-Benedict Calculator (Total Daily Energy Expenditure). Thanks to all authors for creating a page that has been read 590,222 times. Let's calculate the diagonal length of the exemplary rectangle: Naturally, instead of calculating all of these values manually, you can use this area of a rectangle calculator. 3 feet is equal to 36 inches. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in). Moreover, each side of a rectangle has the same length as the one opposite to it. Body shape type is one of the most searched-for problems connected to rectangles. You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Egypt is the leader, but that shouldn't surprise anybody checking the shape of that country on the map. Please pick an option first. Have a look at the table below and check out the first ten countries, as well as the least rectangular ones. WebHeight: When a rectangle is drawn with horizontal and vertical sides, the word height makes it clear which dimension is meant; height labels how high (how tall) the rectangle is. Our decimal degrees to degrees minutes seconds converter can help you convert the angle from decimal degrees to degrees with minutes and seconds. Rewrite as a standard quadratic equation in L A = L * (P / 2 - L) Finally, take the square root of the result: Draw a line from the midpoint of one side of the square to the opposite corner. The calculator will take care of the conversion of values entered in different units. When you encounter a 404 error in WordPress, you have two options for correcting it. Below you'll find a few popular patterns: Of course, tiles come in all shapes and sizes hexagonal and octagonal with squares are quite popular choices. A (area) = L W. Let's determine W from the first equation. Your length is 5 cm and your width is 4 cm, so you should plug them into the equation A = L * W to find the area. (Derivative Approach) 0. To find this rectangle's area, you need to: Convert feet to inches. If you have the diagonal d and width w, it's length is h = (dw). See Also: Find length width rectangle given perimeter Show details Just click. The formula for finding the area of a rectangle is given by Area of a rectangle = Length x Breadth. Polygon diagonals of a rectangle: p = q = (a 2 + b 2) Rectangle Calculations. Note: The angle between diagonals is in the front of the length like in the first figure. EX: Beulah is dedicated to environmental conservation. The easiest way to edit a .htaccess file for most people is through the File Manager in cPanel. For example, if the width of a rectangle is 3 cm, and the length is 4 cm, your formula will look like this: 3 2 + 4 2 = c 2 {\displaystyle 3^ {2}+4^ {2}=c^ {2}} . Multiply the width and length of the rectangle. A rectangle is a 2-dimensional geometrical shape formed by four perpendicular sides. 4. For addon domains, the file must be in public_html/addondomain.com/example/Example/ and the names are case-sensitive. and W by P / 2 - L in A = W * L to obtain Your length is 5 cm and your width is 4 cm, so you should plug them into the equation A = L * W to find the area. Let's start with our rectangle. The outputs are the width, length and diagonal of the rectangle. Square the length and width, then add these numbers together. WebPerimeter of a rectangle. Medium. If you have the perimeter P and width w, its length can be found with h = P/2w. Example 2: Calculate the area of a rectangle whose length and width are 14 cm and 10 cm, respectively. For example, if the width of a rectangle is 3 cm, and the length is 4 cm, your formula will look like this: 3 2 + 4 2 = c 2 {\displaystyle 3^ {2}+4^ {2}=c^ {2}} . Of course, you won't find an ideal rectangle in reality, as it always has a third dimension; but if it's small compared to the other two measurements, the approximation is good enough. We know that, if we decrease the width by 2cm and the length by 5cm, the perimeter will be 18cm. Screens of electronic devices tablets, smartphones, TVs use this area of a rectangle calculator to estimate how much space on the wall your screen will take up or how big the screen of the phone you want to buy is. Put the custom structure back if you had one. Maximum area of a rectangle whose perimeter is $100$. Your expression for the length is then, For example, if you know that area is 24 square centimeters, and that. WebRectangle. The answer is: width of this rectangle is three inches. In this example the image file must be in public_html/cgi-sys/images/. If you're wondering how to find dimensions of a rectangle given area and perimeter, do not fret our dimensions of a rectangle calculator helps you find the dimensions of a rectangle right away. WebArea of Rectangle Formula: The area of a rectangle is determined by the following formula A = a b A = a b where a a and b b are the length and width of the rectangle, respectively. It is possible that you may need to edit the .htaccess file at some point, for various reasons.This section covers how to edit the file in cPanel, but not what may need to be changed. Any combinations will yield a perimeter of 24. Its perimeter is 400m. WebCalculate width & length of a rectangle step by step. Write the length and width next to each other. Draw a circle with a radius equal to that line and center in the midpoint, as in the picture above. Square the length and width, then add these numbers together. [7] A = 4 cm * 5 cm. WebArea = 6 m 3 m = 18 m2 Perimeter of a Rectangle The Perimeter is the distance around the edges. If you have the diagonal d and width w, it's length is h = (dw). If you use the shape tools (ellipse, rectangle, etc.) Step 2: Click on " Calculate " to find the respective length and the width of the rectangle. The area equation is given as A = ab. You can also use it in reverse for example, to calculate the width of a rectangle with a known length and perimeter. To determine the length and width of a rectangle, you need to: Know the area of the rectangle. Decide on the rectangle's width for example. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. Practice: Find the discriminant of the above quadratic equation and find the condition on P and A under which the above problem has no solution. How to Calculate the Area of a Rectangle. WebArea = 6 m 3 m = 18 m2 Perimeter of a Rectangle The Perimeter is the distance around the edges. d = (P - 8 A); Given area and angle: So, the width is 6cm long. How would I find width when I've been given volume, height, and length? Now insert the above equation into the equation for the area (A): The area equation is given as A = ab. Each rectangular shape is characterized by two dimensions, its length, and width. If you want to know more about rectangles and how to find their dimensions, please continue to read the below article. If not, head on to our golden rectangle calculator to learn how you can construct golden rectangles! The formula for finding the area of a rectangle is given by Area of a rectangle = Length x Breadth. Then 2B equals the length. Optimisation problem on area of rectangle. Method 3. That's why our rectangle calculator may be useful not only for math classes but also in your everyday life problems. We know that, if we decrease the width by 2cm and the length by 5cm, the perimeter will be 18cm. A rectangle is a quadrilateral with four right angles. WebThe table top is 1 foot, 9 inches by 1 foot, 5 inches. 16 in = 2 5 in + 2 W Write the length and width next to each other. We and our partners use cookies to Store and/or access information on a device. 1. Below, we provide more calculators that deal with calculations of several rectangle-related parameters. Remember, squaring a number means to multiply the number by itself. WebArea of Rectangle Formula: The area of a rectangle is determined by the following formula A = a b A = a b where a a and b b are the length and width of the rectangle, respectively. Edit the file on your computer and upload it to the server via FTP. If a rectangle is 12 feet long and 6 feet wide, its area is 72 square feet. WebThe formula for finding the area of a rectangle. Sure you can! The properties will tell you the path and file name that cannot be found. Include your email address to get a message when this question is answered. Rectangles have many interesting properties: Other lesser-known rectangular properties: You can think of your own properties as well, e.g., concerning the revolution of a rectangle along the side or diagonal to get a cylinder or a cone, respectively. WebArea of Rectangle Formula: The area of a rectangle is determined by the following formula A = a b A = a b where a a and b b are the length and width of the rectangle, respectively. So, the width is 6cm long. The formula for the perimeter of a rectangle is (width + height) x 2, as seen in the figure below:. d 12 - d 22. This will reset the permalinks and fix the issue in many cases. Sometimes you won't have given the length of two adjacent sides of a rectangle. The area is equal to 4 times 36. Wondering if a square is a rectangle or if a rectangle is a parallelogram? d = l + w, and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: d = (l + w). P = 2 (a + b), For the diagonal of a rectangle: Multiply the width and length of the rectangle. d = (A/l + l) or d = (A/w + w); Given length/width and perimeter: So any combination of numbers that add up to 12 will be our dimensions. Know the perimeter of the rectangle. An example of data being processed may be a unique identifier stored in a cookie. This number divided by 2 is the width. d = (2l - P l + P/4)) or d = (2w - P w + P/4); Given length/width and angle: Drag a dimension shape to the shape you want to measure, and glue the ends of the dimension shape to the points you want to measure. The point where the circle meets the extended square side is the next corner of the golden rectangle. So any combination of numbers that add up to 12 will be our dimensions. As usual, the perimeter is a sum of all sides of a shape: Let's take the same rectangle as an example: The diagonal of a rectangle is a segment that connects two opposite vertices of a rectangle. How to find the correct spelling and folder, 404 Errors After Clicking WordPress Links, From the left-hand navigation menu in WordPress, click. 1. If a rectangle is 12 feet long and 6 feet wide, its area is 72 square feet. The alien civilization calculator explores the existence of extraterrestrial civilizations by comparing two models: the Drake equation and the Astrobiological Copernican Limits. The shape of a rectangle is used in many periodic tessellation patterns. A rectangle is an example of a quadrilateral. This method will only work if you are given the perimeter and length of the rectangle. If you have the area A and width w, its length w is determined as h = A/w. 0. Step 2: Click on " Calculate " to find the respective length and the width of the rectangle. A square is a special case of a rectangle. Answer: Solving the two equations: Area = L B and Perimeter = 2 (L + B), we will get the length and breadth of the rectangle. Its area is 63 square meters. You need two measurements for a rectangle - width and length. To find the area of a rectangle, all you need to do is a multiplication of rectangular sides a and b: Our rectangle calculator has the following formulas implemented: For the perimeter of a rectangle: Just Now Web Now, let the width be w. Since, the length is 4cm greater than the width, the length will be w+4 cm. You can see that to find dimensions of a square, you just have to know either area (. Polygon diagonals of a rectangle: p = q = (a 2 + b 2) Rectangle Calculations. Continue with Recommended Cookies. Each triangle will have sides of length l and w and a hypotenuse of length d. You can use the hypotenuse formula, e.g., from the Pythagorean theorem calculator, to estimate the diagonal of a rectangle, which can be expressed with the following formula: and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: Our diagonal of a rectangle calculator allows you to use almost any units you want. WebHere's how: 1) Write an equation that relates 45cm2, w+4 and w. To do so, we know that the area of the rectangle, 45cm 2 can be found by multiplying w with w+4. This is shown below: 2) Solve the Quadratic Equation. The formula for finding the area of a rectangle is given by Area of a rectangle = Length x Breadth. Instead of using the resizing handles on the table shape to make it smaller, use the Size & Position window to set the exact size. Right click on the X and choose Properties. The word rectangle comes from Latin rectangulus. Hence, we have: To continue, we need to remove the bracket and simplify the equation. Suppose, length of rectangle is 5cm and width is 4 cm, then the area will be: Area = 5cm x 4cm = 20 sq.cm. Finding the maximum perimeter of a rectangle inside of an enclosed region. Have a look at the picture below, and you shouldn't have any doubts about the relations between quadrilaterals anymore: How to read this diagram? Either way, please contact your web host immediately. What I want to Find. WebIn the Shapes window, click More Shapes. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. These are: and two other parameters which are not shown in the picture: The term rectangle comes from the Latin rectangulus, which is a combination of two words: rectus (right, proper) and angulus (angle). WebHow to find the dimensions of a rectangle given the area? For example, you might know that the length is five centimeters longer than the width. How do I calculate the length of a rectangle? The Black Hole Collision Calculator lets you see the effects of a black hole collision, as well as revealing some of the mysteries of black holes, come on in and enjoy! Just plug the area and length of the rectangle into the formula and solve for the width. 1. WebThe formula for finding the area of a rectangle. To find the dimensions of a rectangle: Rewrite the perimeter equation P = 2 (a+b) in terms of one of the dimensions, like so: b = P/2a. For the pentagon, the shape must be irregular to form a tiling pattern. Preview / Show more . d = (a + b). There are many rectangular objects around us. If you do not know the area or the perimeter, or the relationship between the length and the width, you cannot use this method. WebBy multiplying length and breadth, the rectangles area will obtain in a square-unit dimension. Multiply the length times the width. 3. WebThe formula for the area of a rectangle is width x height, as seen in the figure below: All you need are two measurements and you can calculate its perimeter by hand, or by using our perimeter of a rectangle calculator above. The Perimeter is 2 times (a + b): Perimeter = 2 (a+b) Example: A rectangle is 12 cm long and 5 cm tall, what is its Perimeter? [7] A = 4 cm * 5 cm. All you have to do is input the length and width (or diagonal) and allow this rectangle calc to find the values of P (perimeter) and A (area). EX: Beulah is dedicated to environmental conservation. Check out our length converter or area converter to find out how to switch between different units (SI and Calculate A, P, p | Given a, b Given sides lengths a and b calculate area, perimeter and diagonals A = ab; P = 2a + 2b; p = q = (a 2 + b 2) Calculate P, p, b | Given A, a Use this isosceles trapezoid calculator to explore all the various properties of these particular trapezoids. 4. An Australian geo-statistician David Barry calculated the parameter of rectangularity for all countries in the world and created a ranking. Check your result in our area of a rectangle calculator! WebThe table top is 1 foot, 9 inches by 1 foot, 5 inches. /index.php [L] We get 2(l +w) = 24 Dividing both sides by 2, we get l + w = 12 The length and the width must sum up to 12. WebFind the dimensions of a rectangle Math Expression. Hence, we have: To continue, we need to remove the bracket and simplify the equation. WebFind the dimensions of a rectangle Math Expression. In this example, the length is 5 cm and the width is 4 cm. Answer: Solving the two equations: Area = L B and Perimeter = 2 (L + B), we will get the length and breadth of the rectangle. W = 3 in Our diagonal of a rectangle calculator allows you to use almost any units you want. To find this rectangle's area, you need to: The alien civilization calculator explores the existence of extraterrestrial civilizations by comparing two models: the Drake equation and the Astrobiological Copernican Limits. If you go to your temporary url (http://ip/~username/) and get this error, there maybe a problem with the rule set stored in an .htaccess file. But have you ever wondered who's the winner of the most rectangular country competition? WebThe formula for the perimeter of a rectangle is (width + height) x 2, as seen in the figure below: This is the equivalent of adding all four sides, since opposite sides are of equal length by definition. Perimeter = 2 (12 cm + 5 cm) = 2 17 cm = 34 cm Diagonals of a Rectangle If l = 8 and w = 4, then we have 2(8) + 2(4) which simplifies to 16 +8 = 24 Notice that 8 and 4 sum up to 12. When you drag a rectangular table from the Office Furniture stencil, you see that the dimensions are 3 feet, 6 inches by 6 feet. Calculate A, P, p | Given a, b Given sides lengths a and b calculate area, perimeter and diagonals A = ab; P = 2a + 2b; p = q = (a 2 + b 2) Calculate P, p, b | Given A, a Multiply the width and length of the rectangle. WebHow to find the dimensions of a rectangle given the area? For example, if you are trying to find the width of a rectangle that has a perimeter of 22 centimeters, and a length of 8 centimeters, your formula will look like this: For example, for a rectangle with a perimeter of. WebDepending on the dimension to be determined, this rectangle calculator uses the formulas explained here: In case you select to solve for area (A) you have to provide the length (l) and the width (w) then: If you want to calculate the perimeter (P) you have to input the length (l) and the width (w): Let us understand it using an example. Medium. We may also define it in another way: a parallelogram containing a right angle if one angle is right, the others must be the same. and What I want to Find. How do I calculate the length of a rectangle? Also, remember that the diagonal of a rectangle calculator assumes that the length is longer than the width! Any combinations will yield a perimeter of 24. Follow the steps below to find the area: WebFree Rectangle Area & Perimeter Calculator - calculate area & perimeter of a rectangle step by step Make sure the calculation is done using the same unit - the result will also be in that unit, e.g. Then you'll get the information about what your body shape is. As a small thank you, wed like to offer you a $30 gift card (valid at GoNift.com). Right away, you will get the dimensions of the rectangle. WebThis tool will calculate the area of a rectangle from the dimensions of length and width. Before we can find the dimensions of the rectangle, we need find w first. Harris-Benedict calculator uses one of the three most popular BMR formulas. And now let's use that in the second equation: Solving the equation above, we will obtain L. Then, to find W, we can use 3. Optimisation problem on area of rectangle. To find the dimensions of a square with side length a: To find the dimensions of a square with a given area, you just have to take the square root of A. WebIn the Shapes window, click More Shapes. Check out 23 similar 2d geometry calculators , Harris-Benedict Calculator (Total Daily Energy Expenditure), Decimal Degrees to Degrees Minutes Seconds Converter. In this example, the length is 5 cm and the width is 4 cm. Knowing your BMR (basal metabolic weight) may help you make important decisions about your diet and lifestyle. The formulas for the perimeter P and the area A of the rectangle are used to write equations as follows: P = 2 * L + 2 * W. A = L * W. That's it! Example . RewriteRule . If you draw the shape with the pen tool he will not get a size. L = length, d = a + b WebRectangle Formulas Area of a rectangle: A = ab. Instead of using the resizing handles on the table shape to make it smaller, use the Size & Position window to set the exact size. How do find the diagonal of a rectangle given sides? To find the width of a rectangle with a known perimeter and length: Perimeter (P) = 2 length (L) + 2 width (W)

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find the dimensions of the rectangle