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

(a) 10 cm

(b) 12 cm

(c) 9 cm

(d) 8 cm

Explanation:

Let

*ABCD*be the rhombus.

∴

*AB = BC = CD = DA*

Here

*, AC*and

*BD*are the diagonals of

*ABCD,*where

*AC*= 16 cm and

*BD*= 12 cm.

Let the diagonals intersect each other at O.

We know that the diagonals of a rhombus are perpendicular bisectors of each other.

∴ ∆

*AOB*is a right angle triangle, in which

*OA = AC*/2 = 16/2 = 8 cm and

*OB = BD*/2 = 12/2 = 6 cm.

Now,

*AB*[Pythagoras theorem]

^{2}^{ }= OA^{2}+ OB^{2}⇒

*AB*

^{2}= (8)

^{2}+ (6)

^{2}

⇒

*AB*

^{2 }= 64 + 36 = 100

⇒

*AB*= 10 cm

Hence, the side of the rhombus is 10 cm.

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