question_answer

If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, the length of the sides of the rhombus is

A) 9cm

B) 10cm

C) 8cm

D) 20cm

Correct Answer: B

Solution :

We know that, the diagonals of a rhombus are perpendicular bisector of each other. Given, AC = 16 cm and BD = 12 cm   [let]

\[\therefore \,\,\,AO=8\,cm,\,BO=6\,\,cm\] and \[\angle AOB=90{}^\circ\]

In right angled   \[\Delta AOB\],

\[A{{B}^{2}}=A{{O}^{2}}+O{{B}^{2}}\]

[by Pythagoras theorem]

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

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