Answer
$25$ ft.
Work Step by Step
The radius must equal half the diagonal of the square.
If the square has side x, the diagonal is $d=x\sqrt{2}$.
this follows from the Pythagorean relation when we observe the triangle with sides $d, x, x.$
$d^{2}=x^{2}+x^{2}$
$d^{2}=2x^{2}$
Given that $x^{2}=1250$ sq.ft., it follows that
$d^{2}=2500$ sq.ft.
Taking the square root, as d can be be positive only,
$d=50$ ft
Half of that is the wanted radius, $25$ ft.
