The area of a rectangle is 77 ft2 , and the length of the rectangle is 10 ft less than three times the width. find the dimensions of the rectangle.

width (w) = w

Length (L) = 3w - 10

Area (A) = L x w

77 = (3w - 10)w

77 = 3w² - 10w

0 = 3w² - 10w - 77

0 = 3w² - 21w + 11w - 77

0 = 3w(w - 7) + 11(w - 7)

0 = (3w + 11)(w - 7)

0 = 3w + 11, 0 = w - 7

w = , w = 7 (width cannot be negative!)

w = 7

Length (L) = 3w - 10 = 3(7) - 10 = 21 - 10 = 11

width = 7 ft, Length = 11 ft

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