question_answer

The lengths of the diagonals of a rhombus are \[\text{16}\,\text{cm}\] and \[\text{12}\,\text{cm}\]. Then, the length of the side of the rhombus is: (NCERT EXEMPLAR)

A) \[9\,\text{cm}\]

B) \[10\,\text{cm}\]

C) \[8\,\text{cm}\]

D) \[20\,\text{cm}\]

Correct Answer: B

Solution :

[b] We know that, the diagonals of a rhombus are perpendicular bisectors of each other.

Let ABCD be the rhombus such that, \[AC=16cm\]

and          \[BD=12cm\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,AO=8cm,\]

\[BO=6\,cm\] and \[\angle AOB=90{}^\circ \]

In right angled \[\Delta AOB,\]

\[A{{B}^{2}}=A{{O}^{2}}+O{{B}^{2}}\]    (By Pythagoras theorem)

\[\Rightarrow \,\,\,\,\,\,\,\,A{{B}^{2}}={{8}^{2}}+{{6}^{2}}=64+36=100\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,AB=10cm\]