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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 $10\ cm$.
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