question_answer

The lengths of the diagonals of a rhombus are \[24\,m\] and \[10\,m\]. The length of each side of the rhombus is:

A) \[12cm\]

B) \[13cm\]

C) \[14cm\]

D) \[17cm\]

Correct Answer: B

Solution :

[b] Let ABCD be a rhombus, whose diagonals AC and BD bisect each other at O.

Then,    \[OA=12\,cm,\] \[OB=5\,cm\]

and    \[\angle AOB=90{}^\circ ,\]

\[\therefore \]  In \[\Delta AOB,\] by Pythagoras theorem,

\[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}={{(12)}^{2}}+{{(5)}^{2}}=144+25=169\]\[\Rightarrow \,\,\,\,AB=\sqrt{169}=13\,cm.\]

\[\therefore \] The length of each side of rhombus is \[13\,cm.\]