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| Math Central | Quandaries & Queries |
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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,
Penny
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