Choose the correct answer from the given four options:
The lengths of the diagonals of a rhombus are $ 16 \mathrm{~cm} $ and $ 12 \mathrm{~cm} $. Then, the length of the side of the rhombus is
(A) $ 9 \mathrm{~cm} $
(B) $ 10 \mathrm{~cm} $
(C) $ 8 \mathrm{~cm} $
(D) $ 20 \mathrm{~cm} $

Given:

The lengths of the diagonals of a rhombus are \( 16 \mathrm{~cm} \) and \( 12 \mathrm{~cm} \).

To do:

We have to find the length of the side of the rhombus.

Solution:

We know that,

Diagonals of a rhombus are perpendicular bisectors.

From the figure,

$AC=16\ cm$ and $BD=12\ cm$

$\angle AOB=90^o$

$AO=\frac{1}{2}AC$

$=\frac{1}{2}(16)\ cm$

$=8\ cm$

$BO=\frac{1}{2}BD$

$=\frac{1}{2}(12)\ cm$

$=6\ cm$

In right angled triangle AOB, by using Pythagoras theorem,

$AB^2=AO^2+OB^2$

$AB^2=8^2+6^2$

$=64+36$

$=100$

$AB=\sqrt{100}$

$=10\ cm$

The length of the side of the rhombus is $10\ cm$.