Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 160 feet. Find the value(s) for which the area is 2800 square feet.

Answer 1

Let the length of the side parallel to the wall be x. The two perpendicular sides will then each be y in length.

Solve this pair of equations:
x + 2y = 160
x y = 2800

(160-2y)y = 2800
-2y^2 +160y = 2800
y^2 -80y +1400 = 0

Solve for y or factor. It looks to me like the answer is not an integer, there may be two solutions. Use the quadratic equation.

y = [80 + sqrt(800)]/2