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What is the proof called for the fact that the area of a square is always greater than the area of a non-square rectangle of the same perimeter?

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    How about this: "Proof of the fact that area of a square>area of a rectangle of the same perimeter"2012-06-22
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    This is a consequence what is commonly called the arithmetic-geometric mean inequality.2012-06-22
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    This is a consequence of $(a+b)(a-b)=a^2-b^2$.2012-06-22
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    Facts of this kind are sometimes called isoperimetric inequalities, of which the best-known is the fact that the area of a circle is always greater than that of any other region with the same perimeter.2012-06-22
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    Using Lagrange multipliers is one of the approaches you can take. See this link [problem #5]: http://www.math.ualberta.ca/~thillen/math209/s3.pdf2012-06-22

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