Math CentralQuandaries & Queries


Question from Ron, a parent:

I have a 23 acre plot. If it were in a straight line, would it be enough distance for a plane to take off and land if the plane needed 1 mile?


If you have a 23 acre plot, either there is a 1-mile straight line lying within it or there isn't. Theoretically a 23-acre plot, a foot wide, would run for 200 miles (23 acres is about a million square feet and a mile is about 5000 feet). Could be the best little spaghetti farm in Texas!

But a 23-acre plot could also be a square about 1000 feet on a side, and even the diagonal would be only about 1/3 the distance needed.

But the width isn't arbitrary. A runway is typically about 200 ft wide (check Google Maps for your nearest full-scale airport.) And 200ft x 1 mile is just about right.

Good Hunting!



Hi Ron,

You can take an area of 23 acres and form it as a strip of whatever length you want. The question is, if the strip is 1 mile long would it be wide enough for an airplane to land.

One acre is 43 560 square feet so 23 acres is $43 560 \times 23 = 1 001 880$ square feet. A mile is 5280 feet so a rectangular strip of area 1 001 880 square feet and length one mile would be $\large \frac{1 001 880}{5280} = \normalsize 189.75$ feet wide.


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