In the diagram, the length of $D C$ is twice the length of $B D$. The area of the triangle $A B C$ is
(A) 24
(B) 72
(C) 12
(D) 18
(E) 36

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-077.jpg?height=288&width=423&top_left_y=1100&top_left_x=1293)
Since $B D=3$ and $D C$ is twice the length of $B D$, then $D C=6$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-335.jpg?height=296&width=425&top_left_y=1305&top_left_x=904)

Therefore, triangle $A B C$ has a base of length 9 and a height of length 4.

Therefore, the area of triangle $A B C$ is $\frac{1}{2} b h=\frac{1}{2}(9)(4)=\frac{1}{2}(36)=18$.

ANSWER: (D)