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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?

 

 Mar 4, 2021
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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

 Mar 4, 2021

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