Question 564722
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*R^2}}} .
The area for the square is {{{L^2}}} .
We are told that {{{pi*R^2=L^2}}} .
Since length are positive, {{{L=sqrt(pi*R^2)=sqrt(pi)*R}}}
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*pi*R}}} .
We know that, with lengths measured in inches they add up to 360, so
{{{4L+2*pi*R=360}}}
Substituting {{{L=sqrt(pi)*R}}} into the equation above, we get
{{{4sqrt(pi)*R+2*pi*R=360}}} --> {{{(4sqrt(pi)+2*pi)*R=360}}} -->  {{{R=360/(4sqrt(pi)+2*pi)}}}
An approximate value is {{{R=26.92}}} .
That would make the length of wire forming the circle
{{{2*pi*R=2*pi*26.92}}}= approx. 169.1 inches
The length of the other piece, in inches, would be 360-169.1=190.9