Work Step by Step
Since ADE ~ ABC we can assume that AE = AC and DE = CB. We are also told that CE = CB. We can call this X. Then we set up a proportion AE/AC = DE/BC. However we do not know the measure of AC or BC. We plug in 6 + X for AC and X for BC. The resulting proportion is 6/(6+X) = 4/X. Solve and the answer is BC = 12.