Answer
The cost to place fencing around the playground is\[\$5,600\].
Work Step by Step
The cost to enclose field with fencing will be determined by finding the perimeter of the field in the feet. Then, convert the perimeter from feet to yards and multiply the perimeter with the fencing cost given in yards.
Computation of perimeter (P) of the field can be done by using the formula,\[P=2l+2w\]. Length, l is 400 feet and width (w) is 200 feet. Compute the perimeter as shown below:
\[\begin{align}
& P=2l+2w \\
& =2\times 400\text{ ft}+2\times 200\text{ ft} \\
& =800\text{ ft}+400\text{ ft} \\
& =1200\text{ ft}
\end{align}\]
As 3 feet is equivalent to 1 yard so, it is required to convert the value of perimeter in yards to feet using the unit fraction.
\[\frac{1\text{ yd}}{3\text{ ft}}\]
Convert yards into feet as follows:
\[\begin{align}
& 1200\text{ ft}=\frac{1200ft}{1}\times \frac{1yd}{3ft} \\
& =400\text{ yd}
\end{align}\]
For the computation of cost of fencing the field, multiply the perimeter \[400\text{ yd}\] by the cost of $14 per yard.
\[\begin{align}
& \text{Cost}=\frac{400yards}{1}\times \frac{\$14}{yards}\\&=400\times\$14\\&=\$5,600\end{align}\]
Hence, the cost to enclose the field with fencing is\[\$5,600\].
