Three squares are drawn inside a circle as shown. The area of the circle is 60*pi square inches. How many square inches are in the area of one square?
Call the length of each side of the square 'x'.
Draw a line segment from the center of the circle to either of the two points where a square intersects the circle.
There is a right triangle formed by this line segment, one side of a square, and the side formed by two sides of the square.
Since the area of the circle is 60·pi in2 and the formula for the area of a circle is pi·r2:
pi·r2 = 60·pi in2 ---> r = sqrt(60) in
The right triangle (described above) has sides x, 2x, and sqrt(60).
Using the Pythagorean Theorem: x2 + (2x)2 = [ sqrt(60) ]2 ---> x2 + 4x2 = 60
---> 5x2 = 60
---> x2 = 12
---> x = sqrt(12) inches