The area of the square is 
The area of the circle is 

The perimeter of the square is 
The circumference of the circle is 



So  



So  

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

    

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



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:
,      

Second solution
 ,     

We ignore the second solution 

The perimeter of the square is 
The circumference of the circle is 

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