Ann wants to plant a rectangular garden next to a straight river. She has 120 feet of fencing and will not fence the side of the garden next to the river. What dimensions will produce the largest garden?

1 answer

x+2y = 120

A = x y
A = (120-2y)y = 120 y - 2 y^2

2 y^2 -120 y = -A

y^2 -60 y = -A/2

y^2 - 60 y + 900 = -A/2 + 900

(y-30)^2 = -1/2(A -1800)
so y = 30
x = 120 - 60 = 60
sure enough 30*60 = 1800