Question

A square lawn has area 338 ft^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?

The radius of the circle is __ ft.

Answer 1

The area of a square is the length of its side, squared. If a square lawn has area 338, then its side is sqrt(338) = 13sqrt2.

If the sprinkler covers all the way up to the corner of the lawn, we must use the Pythagorean theorem to calculate its radius. If the side of the square is 13sqrt2, then the diagonal of the entire square would be sqrt2*(side length) = sqrt2*13sqrt2 = 2*13 = 26 ft. Then the distance from the center to the corner would be half this diagonal, or 13 ft.

So the radius of the circle is 13 ft.