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.
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.