PQR is a right angled triangle, right angled at R. RS is perpendicular to PQ.

QR = 10 cm and QS = 8 cm. Find PR.

Question

PQR is a right angled triangle, right angled at R RS is
perpendicular to PQ
QR = 10 cm and QS = 8 cm Find PR

Pronay · Accepted Answer

Given : PQR is a right angled triangle right angle at R

RS is perpendicular to PQ

QR=10cm QS=8cm

Now in triangle RQS

${RQ}^{2} = {RS}^{2} + {QS}^{2} \Rightarrow {RS}^{2} = {RQ}^{2} - {QS}^{2} \Rightarrow {RS}^{2} = 10^{2} - 8^{2} \Rightarrow {RS}^{2} = 36 \Rightarrow RS=6cm$

Now as RS is perpendicular to PQ

Therefore

${RS}^{2} = QS \times PS \Rightarrow 6^{2} = 8 \times PS \Rightarrow PS= \frac{36}{8} \Rightarrow PS=4.5 cm$

Therefore PQ=8+4.5=12.5cm

Now in triangle PQR

${PQ}^{2} = {PR}^{2} + {QR}^{2} \Rightarrow {P R}^{2} = {PQ}^{2} - {QR}^{2} \Rightarrow {P R}^{2} = {12.5}^{2} - 10^{2} \Rightarrow {PR}^{2} = 56.25 \Rightarrow PR=7.5cm$

PQR is a right angled triangle, right angled at R. RS is perpendicular to PQ. QR = 10 cm and QS = 8 cm. Find PR.

PQR is a right angled triangle, right angled at R. RS is perpendicular to PQ.

QR = 10 cm and QS = 8 cm. Find PR.