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2

Part of 2017 Math Prize for Girls Problems

Problems(1)

Math Prize 2017 Problem 2

Source:

9/26/2017
In the figure below, BDEFBDEF is a square inscribed in △ABC\triangle ABC. If ABBC=45\frac{AB}{BC} = \frac{4}{5}, what is the area of BDEFBDEF divided by the area of △ABC\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("AA", A, NW), A); dot(Label("BB", B, SW), B); dot(Label("CC", C, SE), C); dot(Label("DD", D, S), D); dot(Label("EE", E, NE), E); dot(Label("FF", F, W), F); [/asy]
Math Prize for Girls