A square lawn has an area of 968 square feet. A sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn.

Question

What is the radius of the circle?

Answer 1

Building on what Jim said:

 

once you've drawn your square inside the circle, divide the square into 2 right triangles.

 

Using the Pythagorean theorem and the dimensions of the square (sqrt 968 on each side) we can figure out the hypotenuse of the triangle:

 

first, get the squares of the two legs of the triangle. They are each sqrt 968 squared, or just plain old 968.

 

968 + 968 = c squared

 

1936 = c squared

 

sqrt 1936 = 44

 

So the hypotenuse of the triangle is 44, and this is also the diameter of the circle, which means that the radius of the circle is 22.

 

hope this helps!

 

Matt

Answer 2

Start by drawing a picture.

 

If the radius of the circle is the distance from the center of the square to the middle of the side of the square, then the circle will be inscribed in the square - but the sprinkler will not reach the corners.

 

If the radius of the circle is the distance from the center of the square to the corner of the square, then the square will be inscribed in the circle and the sprinkler will reach some areas outside of the circle.

The value for the area of the square looks like it fits this model the best.

Circle and Square problems usually come down to either using the Pythagorean theorem or the properties of special triangles - for squares this relates to 45-45-90 triangles.