24. As shown in Figure 3, the diameter $A B=14$ of the semicircle $\Gamma$, the circle $\Gamma^{\prime}$ is tangent to $A B$ at point $P$, and intersects the semicircle $\Gamma$ at points $Q$ and $R, Q R=$ $3 \sqrt{3}, \angle Q P R=60^{\circ}, S_{\triangle P Q R}=\frac{a \sqrt{b}}{c}\left(a 、 b 、 c \in \mathbf{Z}_{+}\right.$, $(a, c)=1$, $\sqrt{b}$ is the simplest radical form). Then the value of $a+b+c$ is $(\quad)$.
(A) 110
(B) 114
(C) 118
(D) 122
(E) 126