Awire 320 in. long is cut into two pieces. one piece is formed into a square and the other 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)? circle in square in

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).

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