Answer
Dimensions are\[200\text{ yd}\]and \[50\text{ yd}\], respectively.
Work Step by Step
The length and width of a rectangular field will be determined by finding the perimeter of the field in the yard.
Computation of length, l and width w of the field by the perimeter can be done by using the formula\[P=2l+2w\]. Length, l is 4 times of the width, w. Compute the length and width as shown below:
\[\begin{align}
& P=2l+2w \\
& =2\left( l+w \right)
\end{align}\]
Substitute the values in the equation above as follows:
\[\begin{align}
& 500\text{ yd}=2\left( 4w+w \right) \\
& 500\text{ yd}=10w \\
& w=\frac{50\text{yd}}{1} \\
& =50\text{ yd}
\end{align}\]
Compute the value of l as mentioned below:
\[\begin{align}
& l=4\times w \\
& =4\times 50\text{ yd} \\
& =200\text{ yd}
\end{align}\]
Hence, the length and width of a rectangular field are \[200\text{ yd}\]and\[50\text{ yd}\], respectively.
