Math, Quadratics
posted by Kelly on .
Farmer John is building a pen to keep his pig in. John has 40m of fencing. He will only need to make 3 sides to the pen because the 4th side will be along a barn. If John wants the maximum area what should the side lengths of the pen be?

L + 2w = 40
so
L = 40  2w
A = L * w
A =(402 w)(w) = 40 w  2 w^2
2 w^2  40 w = A
w^2  20 w = A/2
w^2  20 W + 100 = A/2 + 100
(w10)^2 = (1/2)(A200)
vertex at w = 10, A = 200
so L = 20