Rectangle P Q R S lies in a plane with P Q=R S=2 and Q R=S P=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 ?

**Answer Choices**

A. (2 \sqrt{3}+\sqrt{5}) \pi

B. 6 \pi

C. (3+\sqrt{10}) \pi

D. (\sqrt{3}+2 \sqrt{5}) \pi

E. 2 \sqrt{10} \pi