Geometry Help
 

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?

Perimeter of a Rectangle Example

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:

Formula perimeter of a rectangle

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.

perimeter of rectangle

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.