Question

in the given figure, if pr=12cm, qr=6cm and pl=8cm ,then qm is :

Answer 1

using Pythagoras theorem
QR2=qm2+mr2
(6*6)=(x*x)+(x*x)
36=x2+x2
36=2x2
36/2=x2
18=x2
3underroot 2=x

Answer 2

QM = 4 cm  if pr=12cm, qr=6cm and pl=8cm

Step-by-step explanation:

PR = 12 cm

PL = 8 cm

RL²  = PR² -PL²

=> RL² = 12² - 8²

=> RL² = 144 - 64

=> RL² = 80

=> RL = 4√5 cm

Area of ΔPLR = (1/2) * 8 * 4√5  = 16√5  cm²

LQ = LR - RQ = 4√5 - 6

Area of Δ PLQ = (1/2) 8 * (4√5 - 6)

= 16√5 - 24 cm²

Area of ΔPQR = Area of ΔPLR  - Area of Δ PLQ

=> Area of ΔPQR = 16√5  - (16√5 - 24)  = 24 cm²

Area of ΔPQR = (1/2) * PR * QM  = (1/2) * 12 * QM

= 6 QM

6 QM = 24

=> QM = 4 cm

Another method

Area of Δ PQR  = (1/2) * QR * PL  = (1/2) PR * QM

=> 6 * 8 = 12 * QM

=> QM = 4 cm

Learn more:

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