2015 Cayley Problem 14

In the diagram, \triangle PQR is isosceles with PQ = PR and \triangle PRS is isosceles with PS = SR = x. Also, the perimeter of \triangle PQR is 22, the perimeter of \triangle PRS is 22, and the perimeter of PQRS is 24. What is the value of x?

\textbf{(A)}\ 7.5\quad \textbf{(B)}\ 6.5\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 8

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.