Question

A rectangle has a length of 27 feet less than nine times its width. If the area of the rectangle is 972 find the length of the rectangle

Answer 1

(9x-27)x = 972
9x²-27x = 972
9x²-27x-972 = 0
x²-3x-108 = 0
(x+9)(x-12) = 0
x = -9 or x = 12
Because x has to be >0, thus x = 12 therefore the length of the rectangle is 9(12)-27 = 81