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Math Help - Lagrange Multiplier

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    Lagrange Multiplier

    It seems relatively simple but I still can't get it figure out.

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

    A=\sqrt(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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    Quote Originally Posted by LostMathMan View Post
    It seems relatively simple but I still can't get it figure out.

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

    A=\sqrt(s(s-x)(s-y)(s-z)) where s=p/2 and x, y, z are the lengths of the sides.
    It's easier to maximise A^2 than A. So the problem is to maximise s(sx)(sy)(sz) subject to the constraint x+y+z=2s, where s is constant. (There's also the condition that all the quantities x, y, z, sx, sy, sz should be positive.) That should be a pretty standard Lagrange multiplier problem.
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