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Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of the other diagonal.
Given:
Length of each side of the rhombs$=10\ cm$. Length of one of the diagonals$=16\ cm$.
To do:
We have to find the length of the other diagonal.
Solution:
Let ABCD be the rhombus in which O is the intersecting point of the diagonals.
We know that,
Diagonals of a rhombus bisect each other at right angles.
Therefore,
$\angle BOC=90^o$, $BC=10\ cm$ and $OC=8\ cm$
$\triangle BOC$ is a right-angle triangle.
This implies, using Pythagoras theorem,
$BC^2=BO^2+OC^2$
$(10)^2=(8)^2+OC^2$
$BO^2=(100-64)\ cm^2$
$BO^2=36\ cm^2$
$BO=\sqrt{36}\ cm$
$BO=6\ cm$
$BD=2(BO)=2(6)\ cm$
$BD=12\ cm$
The length of the other diagonal is 12 cm.
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