SOLUTION: 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

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Question 159747: 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 the field is to be completely enclosed within the circle?
Found 2 solutions by edjones, jojo14344:
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
sqrt(1250)=25sqrt(2) length of one side
The diagonal of the field is 25sqrt(2)*sqrt(2)=50' because the hypotenuse of an isosceles right triangle equals the length of one of the sides times sqrt(2) (on the SAT test frequently).
The shortest radius setting is 50/2=25'
.
Ed

Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website!

Remember:
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Now, the shortest radius will point to one corner of the square, so the field will be enclosed to the circle, oks.(draw it to better visualize it I guess)
That radius forms a right triangle where that computed side is cut into half to complete the triangle. Thus the radius now will be the hypotenuse.
.
By Trigo function, in reference to the 45 degree formed now in the corner of the square field:
where , and

therefore,
, ANSWER
thank you,
Jojo