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.