Use Lagrange multipliers to prove that the triangle with maximum area that has a given perimeter p

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Use Lagrange multipliers to prove that the triangle with maximum area that has a given perimeter p is equilateral.

Use Heron’s formula for the area:
A = √s(s - x)(s - y)(s - z)
where s = p/2 and x, y, z are the lengths of the sides.

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