Area=length times width=L*W. L=W+12, because length is 12 ft longer than width, so 120=W(W+12). W^2+12W=120; W^2+12W+36=156, adding 36 to both sides so as to complete the square; (W+6)^2=156, so W+6=sqrt(156)=12.49, so W=6.49 and L=18.49 ft. (The negative square root of 156 would give a negative length for W, so we reject it.). Check: 6.49*18.49=120 approx.