Question

In the given figure, $PR$ is the bisector of $\angle SPQ$. If $PQ=16cm,PS=14cm$ and $QS=18cm$, find $QR$.

• A. $8cm$
• B. $9.6cm$
• C. $10.2cm$
• D. $11.8cm$

Answer 1

The correct option is B $9.6cm$

Given that,

In $△PQR,PR$ is the bisector of $\angle SPQ$

$PQ=16cm,PS=14cm,QS=18cm,$

Let, $QR=k⟹RS=18-k$

By the Vertical angle bisector theorem, we have

$\frac{PQ}{PS}=\frac{QR}{RS}$

$⟹\frac{16}{14}=\frac{k}{18-k}$

$⟹\frac{8}{7}=\frac{k}{18-k}$

$⟹8(18-k)=7k$

$⟹144-8k=7k$

$⟹144=8k+7k$

$⟹144=15k$

$⟹k=\frac{144}{15}=9.6$

$\therefore QR=9.6cm$

Option B is correct.