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How to Find the Length and Width of a Rectangle With a Perimeter and Ratio

The rectangle is a very basic geometric shape. It is defined as a four sided figure where all four internal angles are 90 degrees and opposite sides are the same length. These relationships allow you to solve certain properties of a rectangle using other properties. If you are told the total length around the outside of the rectangle, known as its perimeter, and the ratio between the width and the length, you can come up with two basic equations that will give you the actual width and length of that rectangle.

Things You'll Need

Calculator

Instructions

- 1
  Write out an equation for the perimeter of the rectangle, using x to stand for the width and y for the length. Because a rectangle has two identical widths and two identical lengths, the equation will be Perimeter = 2x + 2y. For example, if your perimeter was 14, you would write 14 = 2x + 2y.
- 2
  Write out an equation for the ratio of the length to the width. This equation will look like Ratio = y/x. In the case of the example, if you were told the ratio is 2.5, you would write 2.5 = y/x.
- 3
  Rearrange the ratio equation to have only y on one side. To do this, you will rewrite it as (Ratio)(x) = y. In the example, this would be 2.5x = y.
- 4
  Rewrite your perimeter equation, substituting the expression (Ratio)(x) in the place of y. Your perimeter equation will then become Perimeter = 2x + 2(Ratio)(x). For the example, your perimeter equation would be 14 = 2x + 2(2.5x).
- 5
  Solve the new perimeter equation for x. This gives you the numerical value of the width of the rectangle. The example equation would be solved by rearranging it to read 14 = 2x + 5x, which is the same as 14 = 7x, and so x = 14/7 = 2.
- 6
  Place the value of width into the ratio equation you made earlier and solve for y. In the example, you would write 2.5(2) = y or y = 5.

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