PreCalculus
posted by Bri .
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.

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
(1602y)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