# 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) $20 \mathrm{~cm}$

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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 $10\ cm$.

Updated on 10-Oct-2022 13:27:48