You have 8L feet of fence to make a rectangular vegetable garden alongside the wall of your house, where L is a positive constant. The wall of the house bounds one side of the vegetable garden. What is the largest possible area for the vegetable garden?

Answer 1

Divide the fence into two equal parts.
Allocate each half to the number of lengths or widths.
8L/2 = 4L
So, assuming the house is along the long side, there is one length and two widths.

Each length is 4L
Each width is 4L/2 = 2L

Thus the maximum area is 4L*2L = 8L^2