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

1430 yards

Explanation:

Note that
`1\text{ acre}=(1)/(640)\text{ square mile}.` Then

`25\text{ acres}=(25)/(640)\text{ square mile}.`

If one side of the restangular field measures exactly
`(1)/(4)` mile, then let the second side be x miles and

`(25)/(640)=(1)/(4)\cdot x,\\ \\x=((25)/(640))/((1)/(4))=(25)/(640)\cdot (4)/(1)=(25)/(160)=(5)/(32)\ mile.`

The perimeter of the rectangle will be

`P=2\cdot (1)/(4)+2\cdot (5)/(32)=(2\cdot 8+10)/(32)=(26)/(32)=(13)/(16)\ mile.`

Since
`1\ mile=1760\ yards,` then
`(13)/(16)\ mile=(13)/(16)\cdot 1760=1430\ yards.`