Your backyard is 21 feet longer than it is wide. Its area is 4720 square feet. Determine its width.

Answer 1

Let's us the variable w to represent the width of the yard. We can write the following expression to represent the length: w + 21

Then area is calculated by multiplying the length by the width. Here that would be:

A = length • width

4720 = (w + 21 ) • w

4720 = w² + 21w

This can be solved for w using factoring as follows:

4720 = w² + 21w

4720 - 4720 = w² + 21w - 4720

0 = w² + 21w - 4720

Since 59 x 80 is 4720, we can factor (w² + 21w - 4720): 0 = (w - 59 ) (w + 80)

Since the width can't be a negative number, w would be 59 feet.

The length would be w + 21 OR 59 + 21 = 80 feet

To verify the area:

A = 59 • 80 = 4720 feet ²