Math CentralQuandaries & Queries


Question from samantha:

What is the distance in miles or how many laps to make a mile, if one was walking around 4 acres of land which is like a square?

Hi Samantha,

There are 43,560 square feet in an acre so 4 acres is $4 \times 43,560 = 174,240$ square feet. If the plot of land is a square with side length $L$ feet then its area is $L^2$ square feet. Thus $L^2 = 174,240$ and hence $L = \sqrt{174,240} = 417.42$ feet. There are 5,280 feet in a mile and

\[\frac{5280}{417.42} = 12.65.\]

Hence 12 times the length of a side of the plot, or 3 laps, is not quite a mile. You would have to go a little more than half the length of a side to complete a mile.

I hope this helps,

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