Question 29
Starting with a paper rectangle measuring $1\times\sqrt2$ metres, Sadako makes one cut to remove the largest possible square, leaving a rectangle. She repeats with the remaining rectangle, producing another square and a smaller rectangle. Since $\sqrt2\approx1.41421356$ is irrational, she can theoretically continue forever. To the nearest centimetre, what is the total perimeter of this infinite pile of squares?