△ABC is similar to△△△ FBE.
△FBE area /△ABC area = (be/BC) 2 (similar triangles's corresponding height ratio is equal to the corresponding side length ratio).
△ABD area /△ABC area =BD/BC (same height but different base)
△FBE area =△ Abd area
(BE/BC)^2=BD/BC
BE^2=BD? In BC, where 2 stands for square.