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| Math Central | Quandaries & Queries |
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Question from LSL, a student: show that of all rectangle with a given area, the square has the smallest perimeter. |
Hi,
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.
Penny
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