SOLUTION: A square lawn has area 338ft^2.  A sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. What is the radius of the​ circle

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Question 1137247: A square lawn has area 338ft^2.  A sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. What is the radius of the​ circle?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A square lawn has area 338ft%5E2.
let the side of lawn be a
  
=>a%5E2=338ft%5E2

if a sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn, the diameter of the​ circle is equal to diagonal of the square which is
d=sqrt%28a%5E2%2Ba%5E2%29
d=sqrt%28338ft%5E2%2B338ft%5E2%29
d=sqrt%28338ft%5E2%2B338ft%5E2%29
d=26ft=> so, radius is r=13ft

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A square lawn has area 338ft^2.  A sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. What is the radius of the​ circle?
If it sprays in a circular motion, usually it will cover the circle that's INSCRIBED in the square. As such, the diameter will be the same length as one of the sides of the square, 

and the radius will be 1%2F2 the diameter, or highlight_green%28matrix%281%2C2%2C+6.5sqrt%282%29%2C+ft%29%29.

However, if it sprays in a circular motion, and covers the entire square lawn, then a situation is created wherein it's covering more than the entire square, which is

INSCRIBED within the CIRCLE. As such, the diameter will be the length of the DIAGONAL of the square, which you would then find, and 1%2F2 of that value will be your radius!.

Therefore, it's NEVER going to JUST cover the lawn. It's either it will cover part of the lawn, or more than the lawn. You determine which it is!