Answer Happy

NOTE: p/4 IS NOT ACCEPTED AS AN ANSWER
Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = xy p = g(x, y) = 2x + 2y Vf(x, y) = (y,x) = Avg = (22,22) Then λ = =-=1/2y = implies that x = Therefore, the rectangle with maximum area is a square with side length