problem on similar triangles 
In the adjacent figure, $\frac{AG}{GD} = \frac{3}{4}$ and $\frac{BD}{DC}=\frac{4}{7}$ and $AE=12 $ cm. Find the length of $EC$.
  1) 33
  2) 36
  3) 44
  4) 48  

Figure:

I think similarity of triangles is to be used but can't really find the target triangles.  

You can use Menelaus' Theorem
$$\frac{BD}{BC}.\frac{CE}{AE}.\frac{AG}{GD}=1\Rightarrow\frac{4}{11}.\frac{CE}{12}.\frac{3}{4}=1$$
