A rectangular room needs 120 square feet of carpet? the width of the room is 2 feet less than its length. find the length and width of the room?

A = LW

A = 120

W = L - 2

120 = L (L-2)

120 = L^2 - 2L

L^2 - 2L - 120 = 0

(L - 12) (L + 10) = 0

L - 12 = 0

L = 12

L + 10 = 0

L = - 10 (extraneous solution ... will not work)

length (L) = 12 ft

width (W) = L - 2 = 12 - 2 = 10 ft