document.write( "Question 564722: a wire 360 in. long is cut into two pieces. one piece is formed into a square, and the other is formed into a circle. if the two figures have the same area, what are the lengths of the two pieces of wire(to the nearest tenth of an inch)? \n" ); document.write( "

Algebra.Com's Answer #365475 by KMST(5328) $\"\"$ $\"About$

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Let L be the length of a side of the square.
\n" ); document.write( "Let R be the radius of the circle.
\n" ); document.write( "The area for the circle is $\"pi%2AR%5E2\"$ .
\n" ); document.write( "The area for the square is $\"L%5E2\"$ .
\n" ); document.write( "We are told that $\"pi%2AR%5E2=L%5E2\"$ .
\n" ); document.write( "Since length are positive, $\"L=sqrt%28pi%2AR%5E2%29=sqrt%28pi%29%2AR\"$
\n" ); document.write( "The length of wire forming the square is the perimeter of the square, $\"4L\"$ .
\n" ); document.write( "The length of wire forming the circle is the circumference of the circle, $\"2%2Api%2AR\"$ .
\n" ); document.write( "We know that, with lengths measured in inches they add up to 360, so
\n" ); document.write( " $\"4L%2B2%2Api%2AR=360\"$
\n" ); document.write( "Substituting $\"L=sqrt%28pi%29%2AR\"$ into the equation above, we get
\n" ); document.write( " $\"4sqrt%28pi%29%2AR%2B2%2Api%2AR=360\"$ --> $\"%284sqrt%28pi%29%2B2%2Api%29%2AR=360\"$ --> $\"R=360%2F%284sqrt%28pi%29%2B2%2Api%29\"$
\n" ); document.write( "An approximate value is $\"R=26.92\"$ .
\n" ); document.write( "That would make the length of wire forming the circle
\n" ); document.write( " $\"2%2Api%2AR=2%2Api%2A26.92\"$ = approx. 169.1 inches
\n" ); document.write( "The length of the other piece, in inches, would be 360-169.1=190.9 \n" ); document.write( "

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