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Question

ABCD is a rhombus. If the length of AC and BD are 16 cm and 12 cm respectively, then find the length of the sides.

A
10 cm
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B
8 cm
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C
6 cm
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D
5 cm
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Solution

The correct option is A 10 cm
Given ABCD is a rhombus.
Hence, AB=BC=CD=DA.
Given, AC=16 cm and BD=12 cm.
Since ABCD is a rhombus, the diagonals AC and BD will be perpendicular bisectors.
Hence, AE=EC=8 cm and BE=ED=6 cm.

Now, we know that,
AEB=BEC=CED=DEA=90°

So, in the triangle AEB, we have
AE=8 cm,BE=6 cm and AEB=90°

By Pythagoreas Theorem,
AE2+BE2=AB2
AB2=82+62=64+36=100
AB2=100
AB=10 cm
Hence, the sides of the rhombus are of length 10 cm.


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