Question

An isosceles triangle $△PQR$, as given, in which the angle bisector $PS$ intersects the line $QR$ at $S$. Also, $PQ=PR$ and $QS=5\text{cm}.$ Find the length of $QR$.

• A. $5$ cm
• B. $10$ cm
• C. $15$ cm
• D. Cannot be determined.

Answer 1

The correct option is B $10$ cm

The given triangle is as follows:

Let us consider $△PQS$ and $△PRS.$

$PS$ is common in both, and as $PS$ is angle bisector of $\angle P$
So, $\angle QPS=\angle RPS$
And $PQ=PR$ (Given)

So,$△PQS\cong △PRS$
(by Side - Angle - Side)

Now, $QS=RS$ (by corresponding parts of congruent triangles)

So, $RS=5$cm
And, $QR=QS+RS$
$QR=5\text{cm}+5\text{cm}$
$QR=10\text{cm}$

Hence, option$\left(b\right)$ correct.