The length of a rectangle is 2 ft more than twice the width. The area is 84 ft2. Find the length and width of the rectangle.

Question

The length of a rectangle is 2 ft more than twice the width. The area is 84 ft². Find the length and width of the rectangle.

Answer 1

The area of a rectangle is lw

lw = 84 ft²

If the length is 2 ft. more than twice the width,

2w + 2 ft = l

Then, as lw = 84 ft²,

(2w + 2 ft)(w) = 84 ft²,

2w² + 2w ft= 84 ft²

2w² + 2w ft - 84 ft² = 0

Divide through by 2; this makes factoring easy

w² + w ft - 42 ft² = 0

(w + 7 ft)(w - 6 ft) = 0

w = 6 ft, - 7ft

The 7 ft answer is invalid

Thus, w = 6 ft

l = 2w + 2 ft = 2(6 ft) + 2ft = 14 ft.

Answer 2

L= 2+2W

LW = 84

(2+2W)W = 84

2W + 2W ^2 = 84

2W^2 + 2W - 84 = 0

W^2 + W - 42 = 0

(W+7)(W-6) =0

W = 6

L= 2(6) + 2 = 14

6 x 14 = 84