If in a triangle PQR, PQ = 4 cm , RP = 6 cm and PS is the angle bisector of the angle P with end S on the side QR, then QS : SR = .

2 : 3

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4 : 5

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3 : 4

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Solution

The correct option is A 2 : 3
We know from angle bisector theorem,
$\frac{P Q}{R P} = \frac{Q S}{S R}$

Given,
PQ = 4 cm
RP = 6 cm
$\frac{P Q}{R P} = \frac{4}{6} = \frac{2}{3}$
$∴ \frac{Q S}{S R} = \frac{2}{3}$
$o r, Q S : S R = 2 : 3$

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