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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The side of rhombus is 56/15cm.
Total number of vertices = 3 = D E and F (Given)
Total number of sided = 3 = AB BC and AC (Given)
AB = 7cm (Given)
BC = 5cm (Given)
AC = 8cm (Given)
AE is the angle bisector of ∠A, thus it divides the sides of the triangle into the proportion as -
= BE:CE = BA:CA = 7:8
Therefore,
= BE:BC = 7 : (7+8)
= 7:15
Since, ΔDBE is similar to ΔABC,
Thus, DE = 7/15 × AC
= DE = 7/15 × 8
DE = 56/15
Thus, the side of rhombus is 56/15cm.
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