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 diag AC = 24 cm and diag BD =18 cm. We know that the diagonals of a rhombus bisect each other at right angles.

\[\therefore \]      \[OA=\frac{1}{2}AC=\left( \frac{1}{2}\times 24 \right)\,\,\text{cm}=12\,\,\text{cm}\]

\[OB=\frac{1}{2}BD=\left( \frac{1}{2}\times 18 \right)\,\,\text{cm}=9\,\,\text{cm}\]

\[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}={{(12)}^{2}}+{{9}^{2}}=(144+81)=225\]      \[\therefore \]\[AB=\sqrt{225}=15\,\,\text{cm}\]

\[\therefore \]Each side of the rhombus is 15 cm.