The lengths of the diagonals of a rhombus are $16\ cm$ and $12\ cm$. Then, find the length of the side of the rhombus.

Given: The lengths of the diagonals of a rhombus are $16\ cm$ and $12\ cm$.

To do: To find the length of the side of the rhombus.

Solution:

Diagonals of rhombus are cut each other at $90^o$.



Since $d_1=16\ cm$ and $d_2=12\ cm$

Therefore, $\frac{d_1}{2}=\frac{16}{2}=8$,

$\frac{d_2}{2}=\frac{12}{2}=6$

Therefore, Using pythagoras theorem, 

$a^2=( \frac{d_1}{2})^2+( \frac{d_2}{2})^2$
 
$\Rightarrow a^2=8^2+6^2$
  
$\Rightarrow a=\sqrt{100}=10\ cm$

Thus, side of the rhombus is $10\ cm$.
 

Updated on: 10-Oct-2022

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