Question

in triangle PQR, PQ is 9cm QR is 14cm PR is 12cm. The bisector of angle PRS meets QR in S. Find QS and RS ?​

Answer 1

Correct Question :

in triangle PQR, PQ is 9cm QR is 14cm PR is 12cm. The bisector of angle PRQ meets QR in S. Find QS and RS ?

Answer :

• PQ is 9 cm

• PR is is 12 cm

• QR is 14 cm

• RS is bisector of angle PRQ and PQ

The line PQ is divided into two equal parts by the bisector . Therefore ,

• PS = QS

• PS = ½PQ

$\longrightarrow\bf{ \dfrac{1}{2}\times 9}$

$\longrightarrow\bf{ 4.5}$

• Therefore PS = 4.5 cm

• Therefore QS = 4.5 cm too .

Here ,

∆ PSR is right angled at S

Therefore ,

• PS is 4.5 cm

• PR is 12 cm

• We have to find RS

Here ,

• PS is base

• PR is hypotenuse

• RS is opposite

By Pythagoras theorem ,

hypo² = base² + opp²

$\longrightarrow\bf{ {12}^{2} = {4.5}^{2} + {opp}^{2}}$

$\longrightarrow\bf{ 144 = 20.25 + {opp}^{2}}$

$\longrightarrow\bf{ 144 - 20.25 = {opp}^{2}}$

$\longrightarrow\bf{ 123.75 = {opp}^{2}}$

$\longrightarrow\bf{ opp = 11.124 }$