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) = Correct: Your answer is correct. p = g(x, y) = Correct: Your answer is correct. ∇f(x, y) = Correct: Your answer is correct. λ∇g = Correct: Your answer is correct. Then λ = 1 2 y = Correct: Your answer is correct. implies that x = Correct: Your answer is correct. . Therefore, the rectangle with maximum area is a square with side length