Suppose x represents the length of fence perpendicular to the house. Then the area of the garden is
area = x(80 -2x)
This is the equation of a parabola that opens downward and has its vertex (maximum) at x=20. (The zeros of area=2x(40 -x) are at x=0 and x=40. The vertex is halfway between them.)
The largest rectangular area that can be enclosed is (20 ft)×(40 ft).
