Question

The total amount of fence around a rectangular play area must be at least 90 feet, but no more than 120 feet. If the length of the play area is twice as long as the width, find the possible widths of the play area.
11 ≤ w ≤ 15
15 ≤ w ≤ 20
21 ≤ w ≤ 30

Answer 1

The perimeter of a triangle has the formula 2l + 2w. Since the length is twice as long as the width, l = 2w. We use this equations to two possible perimeters, 90 and 120 feet.

P = 90 feet
90 = 2(2w) + 2w
90 = 6w
w = 15  feet

P = 120 feet
120 = 2(2w) + 2w
120 = 6w
w = 20

Thus, the range of w is from 15 to 20 feet. The answer is 15 ≤ w ≤ 20