Question 829937
<pre>

The area of the square is {{{s^2}}}
The area of the circle is {{{pi*r^2}}}

The perimeter of the square is {{{4s}}}
The circumference of the circle is {{{2pi*r}}}

{{{(matrix(4,1,Area, of, the, square))}}}{{{""=""}}}{{{(matrix(4,1,Area, of, the, circle))}}}

So  {{{s^2}}}{{{""=""}}}{{{pi*r^2}}}

{{{(matrix(4,1,Perimeter, of, the, square))}}}{{{""+""}}}{{{(matrix(4,1,Circumference, of, the, circle))}}}{{{""=""}}}{{{(matrix(4,1,Length, of, the, wire))}}}

So  {{{4s}}}{{{""+""}}}{{{2pi*r}}}{{{""=""}}}{{{360}}}

That equation can be divided through by 2, so we have

    {{{2s}}}{{{""+""}}}{{{pi*r}}}{{{""=""}}}{{{180}}}

So we have this system of two equations in two unknowns:

{{{system(s^2=pi*r^2,4s+pi*r=180)}}}

Solve the bottom equation for one of the letters and substitute
it in the first equation, getting a quadratic.
You'll get two solutions for (s,r):

First solution:
{{{s = 180/(2+sqrt(pi))=47.71430138}}},   {{{r=180/(2sqrt(pi)+pi)=26.91991183}}}   

Second solution
 {{{s = -180/(sqrt(pi)-2)=791.0483246}}},   {{{r = 180/(pi-2sqrt(pi))=-446.3012248}}}  

We ignore the second solution 

The perimeter of the square is {{{4s = 4*47.71430138=190.8572055)}}}
The circumference of the circle is {{{2pi*r = 2pi*26.91991183 = 169.1427945}}}

As a check add those together and you get 360.

Answers rounded to the nearest tenth of an inch: 

Length of piece formed into a square = 190.9 inches
Length of piece formed into a circle = 169.1 inches 

Edwin</pre>