Question

The length of a rectangle is 8 more than twice its width. The perimeter is 96 feet. Find the length and width of the rectangle.

A) length = 12.5 ft, width = 14.2 ft
B) length = 16.3 ft, width = 11.5 ft
C) length = 25.6 ft, width = 12.2 ft
D) length = 34.6 ft, width = 13.3 ft

Answer 1

The rectangle's width is determined to be 13.3 feet after solving equations involving the defined relationships and the given perimeter. The length is found to be 34.6 feet using the width. Thus, the correct dimensions match with answer choice D.

Step-by-step explanation:

To solve the problem of finding the length and width of the rectangle where the length is 8 more than twice its width, and the perimeter is 96 feet, we start by letting w represent the width of the rectangle. The length l can be expressed as l = 2w + 8. The formula for the perimeter P of a rectangle is P = 2l + 2w. Plugging in the expression for l, we get:

P = 2(2w + 8) + 2w

Solving for w, when P is 96 feet:

96 = 2(2w + 8) + 2w
96 = 4w + 16 + 2w
96 = 6w + 16
80 = 6w
w = 13.3 ft

Now we find the length using the width we just calculated:

l = 2(13.3) + 8 = 26.6 + 8 = 34.6 ft

The dimensions of the rectangle are therefore a width of 13.3 feet and a length of 34.6 feet, which corresponds to answer choice D.