I need help on this word problem. I have had trouble on this for quite some time now.

Question

A gardener wants to create a rectangular vegetable garden in a backyard. She wants it to have a total area of 120 square feet, and it should be 12 feet longer than it is wide. What dimensions should she use for the vegetable garden? Round to the nearest hundredth of a foot.

Answer 1

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.