Perimeter of a Rectangle Example 

Below is a geometry question using the perimeter of a rectangle. In a geometry problem, you may be given the perimeter of a rectangle and the relationship between its width and length. With the perimeter of a rectangle known, you are supposed to calculate the other dimensions of the rectangle.

Using the perimeter of the rectangle to find the other dimensions is a common geometry problem. The example below has the perimeter of a rectangle as 62 inches. However, the same method works whatever the perimeter of the rectangle is and whatever the relationship between its width and length is.

Perimeter of a Rectangle Example: finding width and length of the rectangle

Suppose the perimeter of a rectangle is 62 inches. Let's also suppose that you also know that the length of the rectangle is 1 inch more than twice the width of the rectangle. The geometry question would be, what are the dimensions (i.e. width and length) of the rectangle?

The diagram of the rectangle above marks the length (L) and width (W) of the rectangle. Since we are told that the length (L) is 1 inch more than twice the width, the length is given by L = 2W + 1 (shown in red).

We know from the formula of the perimeter of a rectangle that the perimeter formula is:

Since we know L in terms of W, we are going to substitute L so that we have an algebraic equation with only one unknown, W.

Now we know the width of the rectangle, W, is 10 inches. L is 2W + 1 which gives 21 inches. You can double check your results by putting W and L back in the perimeter of the rectangle equation. The perimeter is 2 (10 + 21) = 62 inches which is what  you started with. So, you know that you have done the calculation right.