College math/bus calc
posted by Hannah on .
A rectangularshaped 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?

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
(y15)^2 = A/2 + 225 = (1/2)(A450)
so y = 15 at vertex
A = 450 at vertex
so
15 by 30 for 450 ft^2 area