Finding the small base length of Trapezoid

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So problem is next: we have a Trapezoid($ABCD$) and we need to find $BC$(small base length). We know only $AD$ wich is big base length(its $10$cm). E point wich is on $AC$(diagonal). $S(abe):S(aed) = 1:2$

This is basically my puzzle... I know its not too complicated but for me i find it difficult so... The main point is finding the $x$ and everything known is on description

It would be great if somebody shows me the way of solving it.

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This is more of a hint:

What can you say about the ratios of the heights from $D$ and $B$ to the diagonal $AC$ using the ratio of the areas?

If you denote $M=AC\bigcap BD$ then what can you san about the ratio $\frac{BM}{MD}$ using the ration of the height as before?

Finally what can you say about the ration $\frac{BC}{AD}$?

The big thing in this problem is to use Tales' theorem which is the same as using similar triangles, so try to fill in the gaps above.