Golden ratio of a circle and square

Question

φ is the golden ratio. In the given figure how can we prove that perimeter of circle is not equal to perimeter of square.

I am confused as it is not clearly described the figure. Then also how can we prove it.

Answer 1

The side of the square is $\sqrt{\phi} \approx 1.272019649 $ and the diameter of the circle is $\phi \approx 1.6180 $ so the perimeter of the square is $4\sqrt{\phi} \approx 5.0880 $ and the circumference of the circle is $\pi\phi \approx 5.0832 $ so close but not equal.