Math CentralQuandaries & Queries


Question from Dee:

I am in the middle of writing the description of the size of a ranch in my story.
It is 3500 acres. How does that equate into mileage? The main ranch house is
at one end, and the foreman's ranch house at the other end.

Hi Dee,

There are 43560 square feet in an acre so the area of your ranch is $43560 \times 3500$ square feet.

From the rough sketch you sent me it looks like you want a roughly rectangular ranch with its length about 5 times its width. Suppose the length is $X$ feet then the width is $5X$ feet. The area of the ranch is then $X \times 5X = 5 X^2$ square feet. Thus

\[5X^2 = 43560 \times 3500\]

and hence

\[X = \sqrt{\frac{43560 \times 3500}{5}} \mbox{ feet.}\]

My calculator gives $X = 5,522$ feet. There are 5,280 feet in a mile so that's $\large \frac{5522}{5280} \normalsize = 1.04$ miles. Hence your ranch is approximately 1 mile by 5 miles.


About Math Central
* Registered trade mark of Imperial Oil Limited. Used under license.


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina Imperial Oil Foundation