The lengths of the diagonals of a rhombus is $24\ cm$ and $10\ cm$. Find each side of the rhombus.
"

Given:

The lengths of the diagonals of a rhombus are $24\ cm$ and $10\ cm$.

To do:

Here, we have to find each side of the rhombus.

 Solution:

We know that,

Diagonals of a rhombus bisect each other at right angles.

Therefore,

$AO = OC = \frac{24}{2}\ cm = 12\ cm$ and $BO = OD = \frac{10}{2}\ cm = 5\ cm$

In $∆AOB$,

By Pythagoras theorem,

$AB^2 = AO^2 + BO^2$

$AB^2= 12^2 + 5^2$

$AB^2= 144 + 25$

$AB^2= 169$

$AB = \sqrt{169} = 13\ cm$

The sides of a rhombus are all equal.

Therefore, $AB = BC = CD = AD = 13\ cm$.

The length of each side of the rhombus is $13\ cm$.

Tutorialspoint

Updated on: 10-Oct-2022

76 Views

Kickstart Your Career

Get certified by completing the course

Get Started