In the diagram, $\triangle P Q R$ is an equilateral triangle. If $P Q=4 x$ and $P R=x+12$, what is the value of $x ?$
(A) 48
(B) 16
(C) 4
(D) 32
(E) 12

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-062.jpg?height=393&width=428&top_left_y=1836&top_left_x=1293)
Since $\triangle P Q R$ is equilateral, then $P Q=Q R=R P$.

Therefore, $4 x=x+12$ or $3 x=12$ and so $x=4$.

ANSWER: (C)