Question

You have to order fencing for a 25-acre, rectangular field. One side of the field measures exactly ¼ mile. How many yards of fencing will you need to enclose the field completely?

Answer 1

Answer:

1430 yards

Step-by-step explanation:

Note that $1\text{ acre}=\dfrac{1}{640}\text{ square mile}.$ Then

$25\text{ acres}=\dfrac{25}{640}\text{ square mile}.$

If one side of the restangular field measures exactly $\dfrac{1}{4}$ mile, then let the second side be x miles and

$\dfrac{25}{640}=\dfrac{1}{4}\cdot x,\\ \\x=\dfrac{\frac{25}{640}}{\frac{1}{4}}=\dfrac{25}{640}\cdot \dfrac{4}{1}=\dfrac{25}{160}=\dfrac{5}{32}\ mile.$

The perimeter of the rectangle will be

$P=2\cdot \dfrac{1}{4}+2\cdot \dfrac{5}{32}=\dfrac{2\cdot 8+10}{32}=\dfrac{26}{32}=\dfrac{13}{16}\ mile.$

Since $1\ mile=1760\ yards,$ then $\dfrac{13}{16}\ mile=\dfrac{13}{16}\cdot 1760=1430\ yards.$