Question

$PS$ is an angle bisector of $\Delta PQR$ and $QS=5\text{ft}.$ What is the length of $QR$?

Answer 1

Let us look at the two triangles
($△PQS$ and $△PRS$) inside $△PQR.$


Side $PS$ is common to both the triangles. $---\left(1\right)$

Also, $PS$ is an angle bisector.

$⟹\angle QPS=\angle RPS---\left(2\right)$

$PQ=PR---\left(3\right)$ (Given)

$⟹△PQS\cong △PRS$

(by the Side-Angle-Side criterion of congruence)

We know that corresponding parts of the congruent triangles are equal.

$⟹QS=RS$

$\therefore RS=5$ ft

$⟹QR=QS+RS=5\text{ft}+5\text{ft}=10\text{ft}$