Math CentralQuandaries & Queries


Question from Ben:


I'm trying to figure out what the length and width of 1 1/3 of an acre would be in a rectangle or in a perfect square


Hi Ben,

One acre is 43,560 square feet. (I'm a Mac user so I asked Siri.) hence 1 1/3 of an acre is

\[\frac{4}{3} \times 43,560 = 58,080 \mbox{ square feet.}\]

If the shape of this region is a square with side length $L$ feet then its area is

\[L^2 = 58,080 \mbox{ and thus } L = \sqrt{58,080} = 241 \mbox{ feet.}\]

If the region is a rectangle of length $L$ feet and width $W$ feet the you know that $L \times W = 58,080$ square feet. There are many values of $L$ and $R$ that will give $L \times W = 58,080.$ For example $L$ could twice $R,$ or three times $R,$ or one and a half times $R.$

I hope this helps,

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