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.

Question

Coke Zero

Mathematics

23 July, 05:01

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.

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Answers (1)

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Xzavier Lozano · Answer 1

3 11/15 cm

Step-by-step explanation:

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