SOLUTION: 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

Algebra ->  Equations -> SOLUTION: 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      Log On


   

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)?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let L be the length of a side of the square.
Let R be the radius of the circle.
The area for the circle is pi%2AR%5E2 .
The area for the square is L%5E2 .
We are told that pi%2AR%5E2=L%5E2 .
Since length are positive, L=sqrt%28pi%2AR%5E2%29=sqrt%28pi%29%2AR
The length of wire forming the square is the perimeter of the square, 4L .
The length of wire forming the circle is the circumference of the circle, 2%2Api%2AR .
We know that, with lengths measured in inches they add up to 360, so
4L%2B2%2Api%2AR=360
Substituting L=sqrt%28pi%29%2AR into the equation above, we get
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
An approximate value is R=26.92 .
That would make the length of wire forming the circle
2%2Api%2AR=2%2Api%2A26.92= approx. 169.1 inches
The length of the other piece, in inches, would be 360-169.1=190.9