question_answer

The lengths of the diagonals of a rhombus are 24 cm and 18 cm, respectively. The length of each side of the rhombus is

A)  12 cm 

B)  9 cm

C)  15 cm 

D)  8 cm

Correct Answer: C

Solution :

Let ABCD be a rhombus in which diagonals AC =24 cm and BD =18 cm. We know that, the diagonals of a rhombus bisect each other at right angles. \[\therefore \]\[OA=\frac{1}{2}AC=\left( \frac{1}{2}\times 24 \right)=12\,\,cm\] \[OB=\frac{1}{2}BD=\left( \frac{1}{2}\times 18 \right)=9\,\,cm\] \[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}={{(12)}^{2}}+{{9}^{2}}\]  \[=144+81=225\] \[\Rightarrow \]\[AB=\sqrt{225}=15\,\,cm\] \[\therefore \]Each side of the rhombus is 15 cm.