The perimeter is
P = 2L + 2W or
80 = 2L + 2W
dividing by 2 we get
40 = L + W
THe area is
A = LW
solving for L, we get
L = 40-W
substituting that in , we get
A = (40-W)(W)
using completing the square, we get
A = -(W-20)^2 + 400
So, when W = 20, the max area is 400.
