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The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The side of the rhombus is:

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12 cm

10 cm

14 cm

16 cm

answer is B.

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Detailed Solution

Let ABCD be a rhombus as shown below.

How to find the length of the diagonal of a rhombus - Advanced Geometry

We know that the diagonals of a rhombus bisect each other at a right angle.

So, in △AED,

AE = 16/2 = 8 cm, ED = 12/2 = 6 cm

So, in ΔAOB, using Pythagoras Theorem, we get

AD² = AE² + ED²

⇒ AD² = 8² + 6²

⇒ AD² = 64 + 36 = 100

⇒ AD = 10 cm

Therefore, the side of the rhombus is 10 cm.

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