Math Question
![Mae is constructing a gravel path around a \( 7 \mathrm{~m} \) by \( 5 \mathrm{~m} \) table, centered in a greenhouse. The path will be the same width, \( x \), on all sides. The length of the greenhouse is \( 2 x+7 \), the width is \( 2 x+5 \), and the area is 99 square meters.
To find the width of the path, Mae multiplied the length and width, and set the product equal to the area. She then simplified the equation and factored out the GCF.
\[
\begin{array}{l}
(2 x+7)(2 x+5)=99 \\
4 x^{2}+24 x-64=0 \\
4\left(x^{2}+6 x-16\right)=0
\end{array}
\]
Complete Mae's solution to find the maximum width of the path.
1 of 12 QUESTIONS
\( 2 \mathrm{~m} \)
\( 4 m \)
\( 16 \mathrm{~m} \)
\( 8 m \)](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2022/4/4/c6967129-46d0-4ea0-b631-312217449877.png "Mae is constructing a gravel path around a \( 7 \mathrm{~m} \) by \( 5 \mathrm{~m} \) table, centered in a greenhouse. The path will be the same width, \( x \), on all sides. The length of the greenhouse is \( 2 x+7 \), the width is \( 2 x+5 \), and the area is 99 square meters.
To find the width of the path, Mae multiplied the length and width, and set the product equal to the area. She then simplified the equation and factored out the GCF.
\[
\begin{array}{l}
(2 x+7)(2 x+5)=99 \\
4 x^{2}+24 x-64=0 \\
4\left(x^{2}+6 x-16\right)=0
\end{array}
\]
Complete Mae's solution to find the maximum width of the path.
1 of 12 QUESTIONS
\( 2 \mathrm{~m} \)
\( 4 m \)
\( 16 \mathrm{~m} \)
\( 8 m \)")
Solution
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