Math CentralQuandaries & Queries


Question from olivia, a student:

If you walk around a building that is 102,869 sq ft, how many miles is that?

Hi Olivia,

It depends on the shape of the building. If the building is long and narrow it is much further around than if it is square. To go to an extreme if the building were 1 foot wide it would be 102,869 feet long and the distance around would be 102,869 + 1 + 102,869 + 1 = 205,740 feet. There are 5,280 feet in a mile so that would be 205,740/5,280 = 39 miles around.

If the building is square it is √102,869 = 320.73 feet on a side. The distance around would be 4 × 320.73 = 1,282.93 feet or 1,282.93/5,280 = 0.24 miles or about a quarter of a mile.


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