Question

In triangle PQR, if PQ = 6 cm, PR = 8 cm, QS = 3 cm, and PS is the bisector of angle QPR, what is the length of SR? (Write answer only in number)

Answer 1

Given:

$\triangle PQR$ with the dimensions as:

PQ = 6 cm

PR = 8 cm

PS is the bisector of $\angle QPR$ such that:

QS = 3 cm

To find:

Length of SR = ?

Solution:

First of all, let us draw the diagram of given dimensions.

Please refer to the attached image.

We can use the angle bisector theorem here, to find the length of SR.

According to Angle Bisector Theorem:

The angle bisector of an angle in a triangle divides the opposite side into two segments which are in proportion to the other two sides.

Applying the above theorem, we can derive the following:

$\dfrac{QS}{SR} =\dfrac{PQ}{PR} \\\Rightarrow \dfrac{3}{SR} =\dfrac{6}{8}\\\Rightarrow \dfrac{3}{SR} =\dfrac{3}{4}\\\\\text{Using Cross Multiplication :}\\\Rightarrow SR =\dfrac{4}{3} \times 3\\\Rightarrow SR =4\ cm$

Hence, the length of SR = 4 cm

Answer 2

Answer:

The length of SR = 4cm

QS/SR=PQ/PR

by putting the values for the above you can get the answer of value 4cm