Why am I getting different results while applying similarity and Pythagoras theorem?

As McFry has said in the comments, the figure is impossible. Suppose we try to construct it. First, we construct right triangle $AED$ with the indicated measurements,and extend segment $AE$ so that $EB$ is $4.2$ units long, as shown:

Now to finish the construction we extend $AD$ and drop a perpendicular from $B$ to $AD$, as shown:

Note that the length of $BC$ is completely determined by the construction so far. In fact, one can determine using similarity that $BC \approx 3.65$. So there is no way to satisfy the conditions of the given diagram, which requires $BC = 8.4$.