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### Section 2.3 : Applications of Linear Equations

9. We want to fence in a field whose length is twice the width and we have 80 feet of fencing material. If we use all the fencing material what would the dimensions of the field be?

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Start Solution

We’ll start by letting $$x$$ be width of the field and so 2$$x$$ will be the length of the field.

Next, we have the following word equation for the length of the fencing material.

$2\left( {{\mbox{Length of Fence}}} \right) + 2\left( {{\mbox{Width of Fence}}} \right) = 80$ Show Step 2

So, plugging all the known information in gives the following equation that we can solve for $$x$$.

\begin{align*}2\left( x \right) + 2\left( {2x} \right) & = 80\\ 6x & = 80\\ x & = 13.33\end{align*}

So, the width of the fence will be 13.33 feet while the length will be 26.66 feet.