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In the diagram, QPS = SPR, PR = 9cm. PQ = 4cm and QS = 3cm, find SR.


Question

In the diagram, QPS = SPR, PR = 9cm. PQ = 4cm and QS = 3cm, find SR.

Options

A) 6\(\frac{3}{4}\)cm

B) 3\(\frac{3}{8}\)cm

C) 4\(\frac{3}{8}\)cm

D) 2\(\frac{3}{8}\)cm

The correct answer is A.

Explanation:

Using angle bisector theorem: line PS bisects angle QPR

QS/QP = SR/PR

3/4 = SR/g

4SR = 27

SR = \(\frac{27}{4}\)

= 6\(\frac{3}{4}\)cm


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