Question

In $△PQR$, seg $RS$ is the bisector of $\angle PRQ,PS=4,SQ=12,PR=13$, find $QR$.

Answer 1

In the given $△PQR$, seg $SR$ is the bisector of $\angle PRQ$ meets $PQ$ at $S$.
$\therefore$ By the angle bisector property of a triangle,
$\frac{PR}{QR}=\frac{PS}{QS}$
$\therefore \frac{13}{QR}=\frac{4}{12}$ (substituting the given values)
$\therefore QR=\frac{13\times 12}{4}$
$\therefore QR=39$ units