Question 1207435
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The square's area is 1250 sq ft.
The side length is sqrt(1250) = 25*sqrt(2) feet.


Half of which is 12.5*sqrt(2) feet.
This is what we have so far
{{{
drawing(400,400,-5,5,-5,5,
line(-3,-3,-3,3),line(-3,3,3,3),line(3,3,3,-3),line(3,-3,-3,-3),line(0,0,3,0),line(0,0,3,3),
circle(0,0,sqrt(18)),

locate(1,-0.2,12.5*sqrt(2)),
locate(3.1,1.5,12.5*sqrt(2)),
locate(1.5,1.5,"x")
)
}}}
We have an isosceles right triangle. Each leg is 12.5*sqrt(2)
The hypotenuse is unknown which I'll call x. This also represents the radius of the smallest possible circle that encloses the square. 


Use the Pythagorean theorem to find x.
I'll let the student finish up.
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