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. = f(x, y) = A = p = g(x, y) = = Vf(x, y) = xvg 000 1 Then λ==y= 2 implies that x = Therefore, the rectangle with maximum area is a square whose side length in terms of p is

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