Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 128 meters

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.