Math CentralQuandaries & Queries


Question from Lynne, a parent:

If a lot's area size is 17,642 square feet, how do I figure the perimeter?

Hi Lynne. There is no exact answer to your question.

Take a look at Penny's reply to this similar question for an explanation of why this is.

All I can tell you is that the rectangle with the smallest perimeter is a square, so if you had a square with that area, it would have sides of the square root of 17,642 square feet, which equals 132.8 feet. That makes the perimeter 531.2 feet. So any rectangular lot with that area will have a perimeter of at least 531 feet.

However, a circular lot with that area would have a smaller perimeter. In fact, this would be the simplest and smallest perimeter possible. We can find the radius of the circle by dividing the area by pi and then taking the square root: sqrt(17,642/3.14159) = 74.94 feet. The perimeter of the circle is 2 times pi times the radius, so (2)(3.14159)(74.94) = 471 feet.

Hope this helps,
Stephen La Rocque.

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