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 (see the figure). What is the shortes

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Question 1207435: 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 (see the figure). What is the shortest radius setting that can be used if the field is to be completely enclosed within the circle?

I need the set up equation.

Thanks.
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description is contradictory to the question.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The side of the square field is  sqrt%281250%29 = 35.35533906 feet, or 35.355 ft rounded.


The diagonal of this square is  35.355%2Asqrt%282%29 ft


The diagonal of this square is the diameter of the circle.


Hence, the radius of the circle is half of that value, or

    r = %2835.355%2F2%29%2Asqrt%282%29 = 25 ft, rounded.    ANSWER

Solved, with complete explanations.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

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

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.