Quadratic word problems

Question

the length of a rectangle is 9 more than the width. the area is 322 square centimeters. Find the length and width of the rectangle

Answer 1

L = W + 9

A = 322 = L * W = W (W + 9) = W² + 9W

0 = W² + 9W - 322

W = (-9 ± √(81 - (4*-322)))/2 = (-9 ± √(81+1288))/2 = (-9 ± √1369)/2 = (-9 ± 37)/2 = -46/2 = -23 or 28/2 = 14

Since the width cannot be negative, the width is 14 and the length 23