# >> K-12 >> Middle School

How to Find Length and Width When You Know the Perimeter & Square Area

Perimeter, area, length and width are four measurements of rectangles. Perimeter is the distance around the edge of the rectangle, area is the length times the width, length is the longer side and width is the shorter side. If you are given the perimeter and area, you can use them, and the following two relationships, to find the length and width. First, the perimeter is twice the length plus twice the width. Second, the area is the length times the width. The reason this method works involves relatively advanced algebra, but it works even if you do not understand the more advanced principles.

Instructions

- 1
  Begin with your known values. Call the perimeter P and the area A. Suppose that P = 100 and A = 400.
- 2
  Divide the perimeter in half. Call this Q. In the example, Q = 50.
- 3
  Square the perimeter, designated by the letter Q. In the example, Q^2 = 50*50 = 2,500.
- 4
  Multiply the area A by four. In the example, 400*4 = 1,600.
- 5
  Subtract the result in step 4 from the result in step 3. In the example, 2,500 - 1,600 = 900.
- 6
  Take the square root of this result. In the example, the square root of 900 equals 30.
- 7
  Subtract this result from Q and divide by 2. In the example, 50 - 30 = 20, and 20/2 = 10. This is the width of the rectangle.
- 8
  Add the result from Step 6 to Q and divide by 2. In the example, 50 + 30 = 80, and 80/2 = 40. This is the length of the rectangle.
- 9
  Check your answer. 40*10 = 400, which is the area that was given, and 40 + 40 + 10 + 10 = 100, which is the perimeter that was given.

How to Find a Function Series of Coordinates

About Aqueducts for Kids