Answer :
Considering the fenced area is a rectangular area, the total fencing is represented by the perimeter of the area, that is:
[tex]\text{perimeter}=2\cdot\text{length}+2\cdot\text{width}[/tex]If the total fencing is 190 yards, we have:
[tex]\begin{gathered} 2\cdot\text{length}+2\cdot\text{width}=190 \\ \text{length}+\text{width}=95 \end{gathered}[/tex]The length is 10 yards more than 8 times the width, so we have:
[tex]\text{length}=10+8\cdot\text{width}[/tex]Using this value of the length in the first equation, we have that:
[tex]\begin{gathered} (10+8\cdot\text{width)}+\text{width}=95 \\ 10+9\cdot\text{width}=95 \\ 9\cdot\text{width}=85 \\ \text{width}=\frac{85}{9}=9.44 \end{gathered}[/tex]Now, finding the value of the length, we have:
[tex]\begin{gathered} \text{length}=10+8\cdot\text{width} \\ \text{length}=10+8\cdot\frac{85}{9} \\ \text{length}=10+\frac{680}{9} \\ \text{length}=\frac{90}{9}+\frac{680}{9}=\frac{770}{9}=85.56 \end{gathered}[/tex]So the dimensions of the fencing are length = 85.56 and width = 9.44.
