Math CentralQuandaries & Queries


Question from kimberly, a student:

is there a relationship between the area and the perimeter of a rectangle?

Hi Kimberley,

If you tell me that the perimeter of a rectangle is $P$ units then I know that the largest area that the rectangle can have is if the rectangle is a square. Its side length would then be $\large \frac{P}{4}$ and its area would be

\[\left( \frac{P}{4}\right)^2 = \frac{P^2}{16} \mbox{ square units.}\]

Other than that all I know is that the area must be positive.

I hope this helps,

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