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The lengths of the diagonals of a rhombus are 24 cm and 10 cm. The length of each side of the rhombus is

(a) 12 cm

(b) 13 cm

(c) 14 cm

(d) 17 cm

Let

*ABCD*be the rhombus with diagonals

*AC*and

*BD*intersecting each other at

*O.*

We have:

*AC*

*= 24 cm and*

*BD*= 10 cm

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

Therefore applying Pythagoras theorem in right-angled triangle

*AOB,*we get:

$A{B}^{2}=A{O}^{2}+B{O}^{2}={12}^{2}+{5}^{2}\phantom{\rule{0ex}{0ex}}=144+25=169\phantom{\rule{0ex}{0ex}}AB=\sqrt{169}=13$

Hence, the length of each side of the rhombus is 13 cm.

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