Question

Your dad is designing a new rectangular garden for your backyard. He has 20 feet of fencing to go around the garden. He wants the length of the garden to be 2½ feet longer than the width. Your dad estimates that the length of the garden will be about 6 feet. Is your dad's estimate reasonable?

Answer 1

Let width = w (ft). Then length = w + 2.5. Perimeter 2(L + w) = 20 ⇒ L + w = 10.

Substitute: (w + 2.5) + w = 10 ⇒ 2w + 2.5 = 10 ⇒ 2w = 7.5 ⇒ w = 3.75 ft.

Then length L = 3.75 + 2.5 = 6.25 ft (6 ft 3 in).

So your dad’s estimate of about 6 feet is reasonable — the actual length is 6.25 ft, only 0.25 ft (3 inches) more.