Math CentralQuandaries & Queries


Question from Angeles:

How many Feet Long In Half An Acre (Rectangle)


To answer this I need to know more about the shape of the rectangle.

For example suppose the rectangle is twice as long as is is wide. If the width is $w$ feet then the length is $2 \times w$ feet and the area is $w \times (2 \times w) = 2 w^2$ square feet. One acre is 43,560 square feet (I asked Siri) and hence

\[2 w^2 = \frac{43560}{2} \mbox{ or } w^2 = 10,890 \mbox{ square feet.}\]

Thus $w = \sqrt{10,890} = 104.36$ feet and the length is $2 \times w = 208.7$ feet.

Now assume the length is 3 times the width and repeat the procedure above. You will find that the length in this case is much different.

Do you know how the width compares to the length?

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