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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.