question_answer

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

A)  10 cm    

B)  12 cm         

C)  9 cm                           

D)  8 cm

Correct Answer: A

Solution :

(a): We know that the diagonals of a rhombus bisect each other at right angles. \[\therefore \]\[OA=8cm,\text{ }OB=6cm\text{ }and\text{ }\angle AOB={{90}^{{}^\circ }}\] \[\therefore \]\[A{{B}^{2}}=\left( O{{A}^{2}}+O{{B}^{2}} \right)=\left( {{8}^{2}}+{{6}^{2}} \right)=\left( 64+36 \right)=100\]                                                                                  \[\Rightarrow \]\[AB=\sqrt{100}=10\]cm So, each side = 10 cm.