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January Question of the Month for Geometry

A 10-foot piece of wire is cut into two pieces.  One piece is bent to form a square.  The other forms a circle inscribed in the square.  How long is each piece?


Solution:

Each side of the square is 2x, so the diameter of the circle is 2x also.  Therefore, the radius of the circle is x.

The perimeter of the square is 8x.

The circumference of the circle is 2(pi)x.

Therefore, 8x+2(pi)x=10

                    (8+2pi)x=10

                               x=.7

So, the length of the piece around the square is .7(8)=5.6 and the piece around the circle is 2(pi).7=4.4.
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