In the given figure, $PQRS$ is a parallelogram, whose diagonals $PR$ and $SQ$ intersect at $O$. $OR=7.5\ cm$ and $SQ$ is $5\ cm$ less than $PR$, find OS."

Given: In the given figure, $PQRS$ is a parallelogram, whose diagonals $PR$ and $SQ$ intersect at $O$. $OR=7.5\ cm$ and $SQ$ is $5\ cm$ less than $PR$.

To do: To find $OS$.

Solution:

$\because$ In parallelograms the diagonals bisect each other.

$OR=7.5$ then $OP$  will also be $7.5$. 

Therefore, $PR=7.5+7.5=15\ cm$

Since $SQ=PR-5$ 

$\Rightarrow SQ=15-5=10\ cm$

$\Rightarrow OQ=OS=\frac{SQ}{2}=5\ cm$

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Updated on: 10-Oct-2022

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