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From the figure PT is an altitude of the triangle PQR in which $P Q = 25 c m, P R = 17 c m$ and $P T = 15 c m$ . If $Q R = x c m$ , then calculate $x$ .

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32 cm

54 cm

28 cm

10 cm

answer is C.

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Detailed Solution

Given that,

P Q = 25 c m, P R = 17 c m

and

P T = 15 c m

.
In right-angled triangle PTQ, apply the Pythagoras theorem, we have

P Q 2 = P T 2 + Q T 2 (25) 2 = (15) 2 + Q T 2 625 − 225 = Q T 2 Q T = 400 Q T = 20

In right-angled triangle PTR, apply the Pythagoras theorem, we have

P T 2 + T R 2 = P R 2 (15) 2 + T R 2 = (17) 2 T R 2 = 289 − 225 T R = 64 T R = 8

Then, the value of x is given by,

Q R = P T + T R = 20 + 8 = 28 c m

Hence, the correct option is 3.

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