Question

In the following figure, in $△PQR,$ seg $RS$ is the bisector of $\angle PRQ,PS=6,SQ=8,PR=15$. Find $QR$.

Answer 1

Given: $RS$ is the bisector of $\angle PRQ$.
$PS=6,SQ=8,PR=15$
To find: $QR=?$
In $△PRQ,RS$ is the bisector of $\angle PRQ$.
By the property of angle bisector of a triangle.
$\frac{PR}{QR}=\frac{PS}{SQ}$
$=\frac{15}{QR}=\frac{6}{8}$
$QR=\frac{15\times 8}{6}=20$