Question

Rhombus $PQRB$ is inscribed in $△ABC$ such that $\angle B$ is one of the its angle, $P$, $Q$ and $R$ lie on $AB$, $AC$ and $BC$ respectively. If $AB=12\text{cm}$ and $BC=6\text{cm}$ find the sides of rhombus $PQRB$.

Answer 1

In $△ABC,PQ||BC$ ......... ($\because$ In a rhombus, opposite sides are parallel)
$\therefore \frac{AP}{AB}=\frac{PQ}{BC}$ ......... (Using Corollary of Thales theorem)
$⟹\frac{12-x}{12}=\frac{x}{6}$
$⟹12x=72-6x$
$⟹18x=72$
$\therefore x=4cm$
The sides of the rhombus is $4$ cm each.