Rhombus adef is inscribed in △abc such that the vertices d, e, and f lie on the sides ab , bc , and ac respectively. find the side of the rhombus if ab=7 cm, bc=5 cm, and ac=8 cm.

3 11/15 cm

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

... BE:CE = BA:CA = 7:8

Then ...

... BE:BC = 7 : (7+8) = 7:15

ΔDBE ~ ΔABC, so DE = 7/15 × AC

... DE = 7/15 × 8 cm = (56/15) cm

... DE = 3 11/15 cm

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