Triangle/Geometry question

Question

How do I solve this triangle question?

In the figure below $\Delta OAB$ has an area of $72$ and $\Delta ODC$ has an area of $288$. Find $x$ and $y$.

Answer 1

As we know: $$16*(16+x)=18*(18+y)$$ And: $$\frac{\frac12*18*16\sin\theta}{\frac12*(18+y)*(16+x)\sin\theta}=\frac{72}{288}=\frac14$$ So: $$x=20,y=14$$