Posted by Shadow on Thursday, December 1, 2011 at 10:34pm.
Considering all rectangles with the same perimeter, the square encloses the greatest area.
Proof: Consider a square of dimensions x by x, the area of which is x^2. Adjusting the dimensions by adding a to one side and subtracting a from the other side 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.
Given 20 meters of fence, the garden is 5 x 5.
*--Considering all rectangles with the same area, the square results in the smallest perimeter for a given area.
*--Given a fixed length of fence, the circle encloses the maximum area.
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