CAYLEY 2015 Problem 14

In the diagram, \triangle{PQR} is isosceles with PQ=PR and \triangle{PRS} is isosceles with PS=SR=x.

Image

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?

Answer Choices
A. 7.5
B. 6.5
C. 7
D. 6
E. 8