Answer:
1430 yards
Step-by-step explanation:
Note that [tex]1\text{ acre}=\dfrac{1}{640}\text{ square mile}.[/tex] Then
[tex]25\text{ acres}=\dfrac{25}{640}\text{ square mile}.[/tex]
If one side of the restangular field measures exactly [tex]\dfrac{1}{4}[/tex] mile, then let the second side be x miles and
[tex]\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.[/tex]
The perimeter of the rectangle will be
[tex]P=2\cdot \dfrac{1}{4}+2\cdot \dfrac{5}{32}=\dfrac{2\cdot 8+10}{32}=\dfrac{26}{32}=\dfrac{13}{16}\ mile.[/tex]
Since [tex]1\ mile=1760\ yards,[/tex] then [tex]\dfrac{13}{16}\ mile=\dfrac{13}{16}\cdot 1760=1430\ yards.[/tex]
