Javascript required
Skip to content Skip to sidebar Skip to footer
Home / How to Find the Length and Width of a Rectangle When Given the Area

How to Find the Length and Width of a Rectangle When Given the Area

Download Article

Download Article

There are numerous ways to find a missing dimension of a rectangle, and the method you use will depend on what information you already have. As long as you know the area or perimeter, as well as the length of one side of the rectangle (or the relationship between the length and width), you can find a missing dimension. The properties of a rectangle are such that you can use these methods for finding the width or length.

  1. 1

  2. 2

    Plug the values for area and length into the formula. Make sure you substitute for the correct variables.

    • For example, if you are trying to find the width of a rectangle that has an area of 24 square centimeters, and a length of 8 centimeters, your formula will look like this:
      24 = 8 w {\displaystyle 24=8w}

  3. 3

    Solve for w {\displaystyle w} . To do this, you need to divide each side of the equation by the length.

  4. 4

    Write your final answer. Don't forget to include the unit of measurement.

  1. 1

  2. 2

    Plug the values for perimeter and length into the formula. Make sure you substitute for the correct variables.

  3. 3

    Solve for w {\displaystyle w} . To do this, you need to subtract the length from each side of the equation, then divide by 2.

  4. 4

    Write your final answer. Don't forget to include the unit of measurement.

  1. 1

  2. 2

    Plug the values for the diagonal and side length into the formula. Make sure you substitute for the correct variables.

    • For example, if you are trying to find the width of a rectangle that has a diagonal length of 5 centimeters, and a side length of 4 centimeters, your formula will look like this: 5 = w 2 + 4 2 {\displaystyle 5={\sqrt {w^{2}+4^{2}}}}

  3. 3

    Square both sides of the formula. You need to do this to get rid of the square root sign, which makes isolating the width variable easier.

  4. 4

    Isolate the w {\displaystyle w} variable. To do this, you need to subtract the squared length from each side of the equation.

  5. 5

    Solve for w {\displaystyle w} . To do this, you need to find the square root of each side of the equation.

  6. 6

    Write your final answer. Don't forget to include the unit of measurement.

  1. 1

    Set up the formula for area or perimeter of a rectangle. Which formula you use will depend on which measurement you are given. If you are given the area, set up the area formula. If you are given the perimeter, set up the perimeter formula.

  2. 2

    Write the expression that describes the relationship between the length and the width. Write your expression in terms of what l {\displaystyle l} equals.

    • The relationship might be given by stating how many times bigger one side is than the other, or how many units more or less it is.
    • For example, you might know that the length is five centimeters longer than the width. Your expression for the length is then l = w + 5 {\displaystyle l=w+5} .

  3. 3

    Replace the l {\displaystyle l} variable in your area (or perimeter) formula with the expression for length. Your formula should now only contain the variable w {\displaystyle w} , which means you can solve for the width.

  4. 4

    Simplify the equation. Your simplified equation might take on various forms, depending on the relationship between the length and the width, and depending on whether you are working with area or perimeter.[7] Think about setting up an equation that allows you to solve for w {\displaystyle w} in the simplest way.

  5. 5

    Solve for w {\displaystyle w} . Again, how you solve for w {\displaystyle w} will depend on your simplified equation. Use the basic rules of algebra and geometry to solve.

Add New Question

  • Question

    How would I find width when I've been given volume, height, and length?

    Blankless X

    Blankless X

    Community Answer

    You divide the volume by the height and the length. You could multiply the height and the length with each other first before dividing. W = V / (H*L).

  • Question

    The length of a rectangle field is twice its breadth. Its perimeter is 400m. How do I find the length and breadth?

    Donagan

    Let B equal the breadth. Then 2B equals the length. Write an equation in B, stating that the perimeter is equal to twice the breadth plus twice the length. Solve for B.

  • Question

    How do I find the area of a rectangle if width and perimeter are given?

    Donagan

    Double the width, and subtract that from the perimeter. Then divide that number by two, which gives you the length of the rectangle. Then, multiply the result by the width to get the area.

  • Question

    How do I find the dimensions of a rectangle if the perimeter is 33 and the length equals twice the width?

    Donagan

    The length (l) is twice the width (w), so l = 2w. The perimeter, or twice the length plus twice the width, is 33, so 2(2w) + 2w = 33. That means 6w = 33; w = 5½, and 2w = l = 11.

  • Question

    Area = 40" and perimeter = 28"; how do I find side lengths of a rectangle?

    Donagan

    Let x and y be the dimensions of the rectangle. Then xy = 40, and 2x + 2y = 28. From the first equation, x = 40/y. Substituting that value of x into the second equation, 2(40/y) + 2y = (80/y) + 2y = 28. Multiply both sides of this equation by y to get rid of the denominator: 80 + 2y² = 28y. Divide by 2 to simplify: 40 + y² = 14y. Subtract 14y from both sides to get zero on one side, and re-arrange slightly: y² - 14y + 40 = 0. Factor the left side: (y - 10)(y - 4) = 0. Set each factor equal to zero to solve for y: y = 4, 10. That means that one side of the rectangle is 4 inches in length, and the other side is 10 inches.

  • Question

    The area is 77 m^2, but all I know about the length is that it's 4 m longer than the width. How do I find the width?

    Donagan

    Set up an equation in which the width (w) is multiplied by four-more-than-the-width (w + 4) to equal 77. Then solve for the width.

  • Question

    How do I find side lengths of a rectangle if only area and perimeter are given?

    Donagan

    Let l and w be the length and width respectively. Set up equations in l and w for the perimeter and the area. Use either equation to solve for l in terms of w, or vice versa, then substitute that value of l into the other equation. That will give you the value of w. Use it in either equation to find the value of l.

  • Question

    One side of a square chessboard is 75 cm; how would I find the area of the board?

    Donagan

    Square the side.

  • Question

    If only area is given, how do I find length and height?

    Donagan

    You cannot find length and width if all you're given is area.

  • Question

    If I am given the area and width, how do I get the length?

    Donagan

    Divide area by width.

Show more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit


Thanks for submitting a tip for review!

About This Article

Article SummaryX

To find the width of a rectangle, use the formula: area = length × width. Just plug the area and length of the rectangle into the formula and solve for the width. If you don't have the area, you can use the rectangle's perimeter instead. In that case, you would use the formula: perimeter = 2 × length plus 2 × width. Plug the perimeter and the length into the formula and solve for the width. To learn how to find the width of a rectangle using the diagonal and the length, scroll down!

Did this summary help you?

Thanks to all authors for creating a page that has been read 523,490 times.

Did this article help you?

How to Find the Length and Width of a Rectangle When Given the Area

Source: https://www.wikihow.com/Find-the-Width-of-a-Rectangle