There is something missing from the question.
As it stands it doesn't have an answer.
Look for the moment at AC, (with C fixed in some way).
Suppose that instead of being told that it's length is 4.1, we are told that it's length is 10 say.
That merely pushes A further from E while having no effect whatever on the length of BC.
It looks like there has to be a relationship between BE and EA.
It say that BA is a perpendicular BISECTOR of DC !
Doesn't that mean that BA "bisects" DC, or cuts it in half? In other words, DE = EC. Triangle DBE is congruent to triangle EBC since they share the perpendicular height of EB, in addition to having DE=EC.
Therefore, BD = BC = 3.7 units.[Diagram is not drawn to scale]. That is my take on it. One of the "Mods" should check this.
