Question

If PR 12cm QR = 6cmand Plegan then QM is​

Answer 1

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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