The coordinates of $\triangle ABC$ are $A(5,7)$, $B(11,7)$, and $C(3,y)$, with $y>7$. The area of $\triangle ABC$ is 12. What is the value of $y$?


$\textbf{(A) }8\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }11\qquad \textbf{(E) }12$
The triangle has base $6,$ which means its height satisfies
\[\dfrac{6h}{2}=3h=12.\]
This means that $h=4,$ so the answer is $7+4=\boxed{(D) 11}$