Math CentralQuandaries & Queries


Question from Bob:

How would I go about finding the maximum area of a rectangle given its perimeter (20m, for example)?

Hi Bob

Suppose the rectangle is $L$ m by $W$ m. Since the perimeter is 20 m, $L + W = 10$ m. The area of the rectangle is $L \times W$ square meters. Solve $L + W = 10$ for $L$ and substitute into the area expression.

Can you complete the solution now?


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