P = 128 meters = 2W + 2L. We want to maximize the area: A = L*W
Solve 128 meters = 2W + 2L for either W or L:
64 meters = W + L, so W = 64-L
and subst. your result into
A = L*W: A = L*(64-L). Then A(L) = 64L - L^2. You could graph this and find the approx value of L at which A(L) is at its max.
Or, if you know calculus, differentiate A(L) and set the result = to 0. Solve for L.
L + W = 64, so you can subst. your value for L into this eqn to find W.
