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We have three sides of a quadrilateral given, each of side length 20.The third side length is known to be less than length 100. Determine the maximum area of such a quadrilateral.

I would guess the answer is when it is a square, but I have no proof. How would we do this?

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    Consider quadrilateral with angles 60,60,120,120 degrees. It's area bigger than square's.2011-11-26
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    In fact, the third side is known to be less than 60. by virtue of the triangle equality.2011-11-26
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    Calculus or no calculus?2011-11-26
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    $$A=\frac{|\tan \theta|}{4}\cdot |a^{2}+c^{2}-b^{2}-d^{2}|$$ , where $\theta$ is intersection angle of the diagonals...2011-11-26

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