I need help to solve this two figures have the same area?

Question

A wire 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 gave the same area, what are the lengths of the two pieces of wire?

Answer 1

320-x is the portion of string for square

x is portion of string for circle, its circumference

square has side measure (320-x)/4 = 80-x/4

area is (80 - x/4)^2

circumference is x=pi*d

so x/pi = d

x/(2*pi) = r

area = pi * [x/(2*pi)]^2 = pi * x^2/(4*pi^2) = x^2/(4*pi)

(80 - x/4)^2 = x^2/(4*pi)

6400 - 40 x + x^2/16 = x^2/(4*pi)

102400*pi - 640*pi x + pi * x^2 = 4 x^2

0 = (4 - pi) x^2 + 640*pi x - 102400*pi

x=150.349

1798.83+ is the area