Question

A rectangular garden has a perimeter of 130 feet. First find an equation for the area of the rectangle as a function of the width, then determine the length and width of the rectangle which provide the maximum area.
Area = A(w) =

Answer 1

P = 2(w+l) = 130, so w+l = 65

Answer 2

Area = w*l, but
w+l = 65, or l = 65-w. Plug that into the area's equation:
A = w*(65-w)

Answer 3

Maximize area:
A = -w^2 + 65w
A' = -2w+65 = 0
-2w=-65
w = 32.5

Answer 4

l = 65-32.5 = 32.5

Answer 5

Max area = 32.5^2