A rectangular-shaped garden has one side along the side of a house. the other three sides are to be enclosed with 60ft of fencing. what is the largest possible area of such a garden?

Answer 1

x = length
y = width
A = x y
P = 60 = x + 2 y
so
x = 60 - 2 y

A = (60 - 2 y) y = 60 y - 2 y^2

2 y^2 - 60 y = -A
y^2 - 30 y = -A/2
complete square for vertex of parabola
y^2 - 30 y + 225 = -A/2 + 225
(y-15)^2 = -A/2 + 225 = -(1/2)(A-450)
so y = 15 at vertex
A = 450 at vertex
so
15 by 30 for 450 ft^2 area