Question

In $△PQR,AB\parallel QB$. If $AB$ is $3cm,PB$ is $2cm$ and $PR$ is $6cm$, then find the length $QR$

Answer 1

Given $AB$ is $3cm,PR$ is $2cmPR$ is $6cm$
In $△PAB$ and $△PQR$
$\angle PAB=\angle PQR$ (corresponding angles)
and $\angle P$ is common.
$\therefore △PAB\sim △PQR$ ($AA$ similarity criterion)
Since corresponding sides are proportional,
$\frac{AB}{QR}=\frac{PB}{PR}$
$QR=\frac{AB\times PR}{PB}$
$=\frac{3\times 6}{2}$
Thus, $QR=9cm$.