The area of a circle can be computed from the circumference (c) as
.. Acircle = c^2/(4π)
The area of a square can be computed from its perimeter (p) as
.. Asquare = (p/4)^2 = p^2/16
These are equal when
.. Acircle = Asquare
.. c^2/(4π) = p^2/16
.. c^2/p^2 = (4π)/16
.. c/p = (√π)/2
The total length is 320 inches, so ...
.. wire for circle = ((√π)/2)/(1 +(√π)/2)*320 in ≈ 150.3 in
.. wire for square = 320 in - wire for circle ≈ 169.7 in
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In the graph, (x, y) represents (circle wire, square wire).
