Question

in triangle PQR seg PS is a bisector of angle QPR. QS=6cm SR=8cm PQ=15cm find PR

Answer 1

Answer:

Value of side PR is 20 cm.

Step-by-step explanation:

In the ΔPQR , PS is the bisector of ∠QPR.

We have to find the length of side PR.

to find the length of side PR let PR= x cm

Angle bisector theorem stated as Let in a triangle XYZ, bisector of angle X meets YZ at M then the ratio of the length of  YM to the length of MZ is equal to the ratio of the length of side XY to the length of side XZ.

Here, bisector of ∠QPR meets QR at S.

Using angle bisector theorem,

$\frac{QS}{SR}=\frac{PQ}{PR}$

$\frac{QS}{SR}=\frac{PQ}{PR}$

Substitute the values,

$\frac{6}{8}=\frac{15}{x}$

Solving for x , we get

$x \times 6=8 \times 15$

$\Rightarrow x=\frac{8 \times15}{6}$

$\Rightarrow x=20$

Thus, value of side PR is 20 cm.