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 Question from kimberly, a student: is there a relationship between the area and the perimeter of a rectangle? explain.

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,
Penny

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