One side of the rectangular field measures 1/4 miles.
Let x = the length of the other side in miles.
Then the area of the field is
A = 0.25x mi²
Note that
1 mi² = 640 acres, or 1/640 mi²/acre.
The area is given as 25 acres, which is equal to
(25 acres)*(1/640 mi²/acre) = 0.0391 mi²
Therefore
0.25x = 0.0391
x = 0.1563 mi
The length of fencing required is the perimeter of the rectangle.
It is
2*(0.1563 + 0.25) = 0.8126mi.
Because 1 mile = 1760yards, therefore the perimeter is
0.8126*1760 = 1430.2 yds
Answer: 1430.2 yards
For practical purposes, it should be 1431 yards.