MCQ practice · SSC General Mathematics Board questions · Chapter 6: Lines, Angles and Triangles
In the right-angled triangle PQR, ∠Q = 1 right angle and ∠P = 2∠R. Which of the following is correct?
Think it through first, then pick an option.
- a PR = 2QR
- b PQ = 2PR
- c PR = 2PQ
- d QR = 2PQ
Answer and explanation
Correct answer: c PR = 2PQ
∠R = 30° and ∠P = 60°; the side PQ opposite ∠R is half the hypotenuse PR, so PR = 2PQ.
Why the other options are wrong
- a PR = 2QR: PR = 2QR is wrong; the side opposite ∠R = 30° is PQ, not QR.
- b PQ = 2PR: PQ = 2PR would make PQ longer than the hypotenuse, which is impossible.
- d QR = 2PQ: QR = 2PQ would make QR equal to PR, but the hypotenuse is longer than QR.
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