Find the dimensions of the rectangle with perimeter 200 mete

Solution

If we have a length l and width w, we have: A = l*w P = 2l + 2w = 200 l + w = 100 l = 100 - w Now plug this into the first equation: A = l*w = (100 - w)w = 100w - w^2 Now we take a derivative and set it equal to 0: 0 = 100 - 2w 2w = 100 w = 50 So the max is a square with sides of 50 m