MathDB

In the figure below,

BDEF

is a square inscribed in

\triangle ABC

. If

\frac{AB}{BC} = \frac{4}{5}

, what is the area of

BDEF

divided by the area of

\triangle ABC

? [asy] unitsize(20); pair A = (0, 3); pair B = (0, 0); pair C = (4, 0); draw(A -- B -- C -- cycle); real w = 12.0 / 7; pair D = (w, 0); pair E = (w, w); pair F = (0, w); draw(D -- E -- F); dot(Label("

A

", A, NW), A); dot(Label("

B

", B, SW), B); dot(Label("

C

", C, SE), C); dot(Label("

D

", D, S), D); dot(Label("

E

", E, NE), E); dot(Label("

F

", F, W), F); [/asy]

Problem Statement