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?
Name of proof that area of square>area of rectangle of the same perimeter
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$\begingroup$
geometry
algebra-precalculus
terminology
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2How 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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2This is a consequence what is commonly called the arithmetic-geometric mean inequality. – 2012-06-22
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0This is a consequence of $(a+b)(a-b)=a^2-b^2$. – 2012-06-22
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4Facts 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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0Using Lagrange multipliers is one of the approaches you can take. See this link [problem #5]: http://www.math.ualberta.ca/~thillen/math209/s3.pdf – 2012-06-22