You have 4L 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

Perimater=4L=2width+1length
or length=4L-2w

area=width(4L-2W)

darea/dw=(4L-2w) + w(-2)=0
width=L
length=2L

check my thinking

Answer 2

looks correct. The fence is divided equally among lengths and widths.

Answer 3

yes 2L^2 is correct