2008 AMC 10A Question 19 - thichhoctoan.com

Question 19

Rectangle $PQRS$ lies in a plane with $PQ = RS = 2$ and $QR = SP = 6.$ The rectangle is rotated $90^\circ$ clockwise about $R,$ then rotated $90^\circ$ clockwise about the point that $S$ moved to after the first rotation. What is the length of the path traveled by point $P?$

$\left(2\sqrt{3} + \sqrt{5}\right)\pi$
$6\pi$
$\left(3 + \sqrt{10}\right)\pi$
$\left(\sqrt{3} + 2\sqrt{5}\right)\pi$
$2\sqrt{10}\pi$