Let's use the variable x to represent the width of the field.
If the length is 38 yd longer thatn the width, the length is equal to "x + 38".
Then, if the perimeter (which is the sum of all sides) is equal to 160 yd, we can write the following equation:
[tex]\begin{gathered} \text{Perimeter}=2\cdot\text{length}+2\cdot\text{width} \\ 160=2\cdot(x+38)+2\cdot x \end{gathered}[/tex]Solving this equation for x, we have:
[tex]\begin{gathered} 80=x+38+x \\ 2x+38=80 \\ 2x=80-38 \\ 2x=42 \\ x=\frac{42}{2} \\ x=21\text{ yd} \\ \\ \text{length}=x+38=21+38=59\text{ yd} \end{gathered}[/tex]Therefore the length is equal to 59 yd and the width is equal to 21 yd.
