Help quick please

Question

The length of a rectangular storage room is 9 feet longer than it’s width. If the area of the room is 90 square feet, find its dimensions.

Answer 1

L = W + 9

A = 90 = L * W = (W + 9) * W = W² + 9W -> 0 = W² + 9W - 90 = (W + x) * (W - y)

The factors of 90 are 2*3*3*5 and we want 2 combinations of the factors that if 1 is positive and the other negative makes 9. With a little experimentation, the only possible values of x and y are -6 and 15 which means the possible values for W are 6 and -15. Since the room cannot have a negative width, the width is 6 and length is 15.