Question 187800
An adjustable water sprinkler that sprays water in a circular pattern is placed at the center of a square field whose area is 1250 square feet. What is the shortest radius setting that can be used if all of the grass is to be watered?
:
We want to find the diagonal (d) of the square, that would be the diameter
 of the circular watered area. The radius would be half of that.
:
Since it's a square, the side dimensions would be:
s = {{{sqrt(1250)}}}
then we square that to find the hypotenuse: d^2 = s^2 + s^2, so we have:
d^2 = 1250 + 1250
d = {{{sqrt(2500)}}}
d = 50 ft
then
r = 25 ft is the minimum radius of the sprinkler