a rectangle of perimeter 100 units has the dimensions shown. Its area is given by the function A = w(50 - w). What is the GREATEST area such a rectangle can have?
P = 2 W + 2 L 100 = 2 W + 2 L /:2 50 = W + L A = W ( 50 - W ) = 50 W - W² A` (W) = 50 - 2 W 50 - 2 W = 0 2 W = 50 W = 50 : 2 W = 25; L = 50 - 25 = 25 The greatest area such a rectangle can have: A = 25 * 25 = 625 units²
