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October 22, 2014

October 22, 2014

Posted by **lily** on Sunday, March 20, 2011 at 5:15pm.

- geometry -
**tchrwill**, Monday, March 21, 2011 at 9:40amConsidering all possible rectangles with a given perimeter, the square encloses the greatest area.

Proof:

Consider a square of dimensions "x "by "x", the area of which is x^2.

Adjust the dimensions by adding "a" to one side and subtracting "a" from the other side.

This results in an area of (x + a)(x - a) = x^2 - a^2.

Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.

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