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?

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 = - , w = 4

Since width cannot be negative, disregard -

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

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