△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.