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

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) (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 .
The area for the square is .
We are told that .
Since length are positive,
The length of wire forming the square is the perimeter of the square, .
The length of wire forming the circle is the circumference of the circle, .
We know that, with lengths measured in inches they add up to 360, so

Substituting into the equation above, we get
--> -->
An approximate value is .
That would make the length of wire forming the circle
= approx. 169.1 inches
The length of the other piece, in inches, would be 360-169.1=190.9
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