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Question

# ABCD is rhombus. If the length of AC and BD are 8 cm and 6 cm respectively, then find the length of the sides.

A
3 cm
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B
4 cm
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C
5 cm
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D
6 cm
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Solution

## The correct option is C 5 cm Given ABCD is a rhombus. Hence, AB = BC = CD = DA. Given, AC = 8 cm and BD = 6 cm. Since, ABCD is a rhombus, the diagonals AC and BD will be perpendicular bisectors. Hence, AE = EC = 4 cm and BE = ED = 3 cm. Now, we know that, ∠AEB=∠BEC=∠CED=∠DEA=90° So, in the triangle AEB, AE=4 cm,BE=3 cm and ∠AEB=90° By Pythagoreas Theorem, AE2+BE2=AB2⇒AB2=42+32=16+9=25⇒AB2=25⇒AB=5 cm Hence, the sides of the rhombus are of length 5 cm.

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