In triangle ABC,R is the mid-point of BC,CS=3SA, and \displaystyle\frac{AT}{TB}=\frac pq. If w is the area of \triangle{CRS},x is the area of \triangle{RBT},z is the area of \triangle{ATS}, and x^2=wz, then the value of \frac pq is
Answer Choices
A. \frac{\sqrt{21}-3}{2}
B. \frac{\sqrt{21}+3}{2}
C. \frac{\sqrt{21}-3}{6}
D. \frac{\sqrt{105}+3}{6}
E. \frac{\sqrt{105}-3}{6}