Math CentralQuandaries & Queries


Question from Chuck:

How far do I walk when I walk around a 751,000 sq. ft. warehouse?

Hi Chuck,

The answer depends on the shape of the warehouse. I expect it is rectangular and if the sides are the same length, say $x$ feet long so it is a square then the area is $x^2$ square feet so you have

\[x^2 = 751,000 \mbox{ square feet}\]

and hence

\[x = \sqrt{751,000} = 866.6 \mbox{ feet.}\]

Thus the distance around the warehouse would be $4 \times 866.6 = 3,466$ feet.

If the warehouse is 3 times as long as it is wide and the width is $x$ feet then the area would be

\[3x^2 = 751,000 \mbox{ square feet}\]

and thus

\[x = \sqrt {\frac{751,000}{3}} = 500.3 \mbox{ feet.}\]

In this case the distance around the warehouse would be $8 \times 500.3 = 4,002$ feet.

Without knowing more about the shape of the warehouse I can't give you an exact answer.


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