Question

The length of a rectangle is 1 less than twice the width. The area of the rectangle is 28 square feet. What is the length of the rectangle?

Answer 1

Length (L): 2w - 1

width (w): w

Area (A) = L · w

28 = (2w - 1) · (w)

28 = 2w² - w

0 = 2w² - w - 28

0 = 2w² - 8w + 7w - 28

0 = 2w(w - 4) + 7(w - 4)

0 = (2w + 7) (w - 4)

2w + 7 = 0 , w - 4 = 0

w = -$\frac{7}{2}$ , w = 4

Since width cannot be negative, disregard -$\frac{7}{2}$

Length (L) = 2w -1 → L = 2(4) - 1 → L = 8 - 1 → L = 7

Answer: 7