https://www.gregmat.com/quizzes/quiz/gre-quant-flashcards-group-9-quiz (Question 15)
How is BE the same as BC…
They’re not the same. In fact, BC < BD < BE. The two quantities are, however, the same because the area is a function of a triangle’s base and height. Two triangles can conceivably have the exact same area without having the same side lengths, which is what is happening here since they share base BC and have the same perpendicular height.