Lw = Area
2L + 2w = 360
L = 180 - w
(180-w)w = Area = A(w) is a function of width w
The zeros of this function is w=0 and w=180.
The max occurs at the average of the zeros, which is 90.
L = 180 - 90 = 90
w = 90
Max area occurs with dimensions L=w=90, which is really a square.
Max area is 8100