Math CentralQuandaries & Queries


Question from LSL, a student:

show that of all rectangle with a given area, the square has the smallest perimeter.


If a rectangle has dimensions x units by y units then its perimeter is P = 2x + 2y and its area is A = xy square units so y = A/x. Substitute y = A/x into the expression for the perimeter and use the calculus you know to minimize this expression. Remember that A is a constant.


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