The area of a rectangle is 99 in². The length of the rectangle is 2 in. longer than the width.

What is the width of the rectangle?

A = L * W

A = 99

L = W + 2

99 = W (W + 2)

99 = W^2 + 2W

W^2 + 2W - 99 = 0

(W - 9) (W + 11) = 0

W - 9 = 0

W = 9

W + 11 = 0

W = - 11 (extraneous solution ... this one does not work)

L = W + 2

L = 9 + 2

L = 11

check ...

A = L * W

99 = 11 * 9

99 = 99 (correct)

so the length (L) = 11 and the width (W) = 9