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The lengths of the diagonals of a rhombus are $30\ cm$ and $40\ cm$. Find the sides of the rhombus.
Given: The lengths of the diagonals of a rhombus are $30\ cm$ and $40\ cm$.
To do: To find the sides of the rhombus.
Solution:
Let $ABCD$ be a rhombus and $AC$ and $BD$ be the diagonals of $ABCD$.
So, $AC=30\ cm$ and $BD=40\ cm$
We know that diagonals of a rhombus bisect each other at right angle.
$\therefore AO=OC=15\ cm$ and $BO=OD=20\ cm$
In $\vartriangle AOB$, Using Pythagoras theorem, we have
$AB^2=AO^2+BO^2$
$=15^2+20^2$
$=225+400$
$=625$
$\Rightarrow AB=\sqrt{625}=25\ cm$
Since, the sides of rhombus are all equal.
Therefore, $AB=BC=CD=AD=25\ cm$.
Updated on: 10-Oct-2022
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