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

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6 cm

9 cm

4 cm

2 cm

answer is C.

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Detailed Solution

Given, a figure of triangle as PR = 12 cm, QR = 6 cm and PL = 8 cm.
Here, we have to find the length of QM.
So, in

△ P L R

and

△ Q M R

, we have,

∠ P L R = ∠ Q M R = 90 °

∠ R = ∠ R

(Common for both triangles).
So, by the AA similarity criteria, we can say that,

△ P L R ≈ △ Q M R

Then, we have,

P L P R = Q M Q R 812 = Q M 6 4 = Q M Q M = 4 cm

So, the length of the perpendicular QM is obtained as 4 cm.
Hence, the correct option is (3).

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