Question

In figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is



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Answer 1

Given:

PR = 12 cm, QR = 6 cm and PL = 8 cm.

(i) In right angled triangle APLR

PR² = PL² + LR² [Using Pythagoras theorem]

⇒ LR² = PR² - PL²

⇒ LR² = 144 - 64

⇒ LR² = 80

⇒ LR = 4√5 cm

Now,

LR = LQ - QR

    = 4√5 - 6 cm

(ii) In right angled triangle PLR,

A₁ = (1/2) * LR * PL

   = (1/2) * (4√5) * 8

   = 16√5 cm

(iii) In right angled triangle PLQ,

A₂ = (1/2) * LQ * PL

    = (1/2) * (4√5 - 6) * 8

    = 16√5 - 24

Now,

Area of ΔPLR = Area of ΔPLQ + Area of ΔPQR

⇒ 16√5 = (16√5 - 24) + Area of ΔPQR

⇒ 24 = Area of ΔPQR

⇒ 24 = (1/2) * PR * QM

⇒ 24 = (1/2) * 12 * QM

⇒ QM = 4 cm

Hope it helps!