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Question

In the given figure, PR is the bisector of SPQ. If PQ=16 cm,PS=14 cm and QS=18 cm, find QR.
1183099_3ca54da97c754b64873d77334ae347f6.png

A
8 cm
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B
9.6 cm
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C
10.2 cm
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D
11.8 cm
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Solution

The correct option is B 9.6 cm
Given that,
In PQR,PR is the bisector of SPQ
PQ=16 cm,PS=14 cm,QS=18 cm,

Let, QR=kRS=18k

By the Vertical angle bisector theorem, we have
PQPS=QRRS

1614=k18k

87=k18k

8(18k)=7k

1448k=7k

144=8k+7k

144=15k

k=14415=9.6

QR=9.6 cm

Option B is correct.



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