Ernie wants to fence in a rectangular play yard for his two dogs. He has 12 pieces of fence that are one unit each. What are the dimensions of the largest play yard that Ernie could make? Show your work

Answer 1

2 L + 2 w = 12 so L = 6-w
area = A = L w

L w = (6-w)w = A

w^2 - 6 w = -A
find vertex by completing square

w^2 - 6 w + 9 = -A+9

(w-3) = -1(A-9)
max at w = L =3 and area = 9

By the way, you could have guessed that our rectangle would turn out to be a square.