Question

In triangle pqr , if pq=6cm pr = 8cm qs =3cm and ps is the bisector of angle qpr , what is the length of sr?

Answer 1

Answer:

Explanation:

Since, PS is the angle bisector of angle QPR

So, by angle bisector theorem,

QS/SR = PQ/PR

⇒ 3/SR = 6/8

⇒ SR = (3 X 8)/6 cm = 4 cm

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Answer 2

Given :- In triangle PQR, PQ = 6 cm, QS = 3 cm, PR = 8cm and PS is the bisector of angle QPR .

To Find :- The length of SR = ?

Concept used :-

• Angle bisector theorem :- An angle bisector in a triangle divides the opposite side in the same ratio as the other two sides of the triangle .

Solution :-

In ∆PQR, given that, PS is the angle bisector of ∠QPR .

So, PS cuts side QR at S .

then,

→ PQ/PR = QS/SR { By angle bisector theorem }

putting given values we get,

→ 6/8 = 3/SR

→ 6 * SR = 8 * 3

→ 6 * SR = 24

dividing both sides by 6,

→ SR = 4 cm (Ans.)

Hence, Length of SR is equal to 4 cm .

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