Question

In the given figure, PQ = PR, and $PS$ is an angle bisector of $\angle PQR$. If $QS=6\text{ft}$, what is the length of $QR$?

• A. 12 ft
• B. 6 ft
• C. 18 ft
• D. 10 ft

Answer 1

The correct option is A 12 ft

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


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

Also, $PS$ is the angle bisector.

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

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

$⟹\Delta PQS\cong \Delta PRS$
(by S-A-S criterion of congruence)

$⟹QS=RS$
(as corresponding parts of congruent triangles)

$\therefore RS=6$ ft

$⟹QR=QS+RS=6\text{ft}+6\text{ft}=12\text{ft}$