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If in ΔPQR, ∠P = 70^o and ∠Q = 75^o, then which of the following relations is correct?

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PQ > QR > PR

PQ > PR > QR

QR > PR > PQ

PR > QR > PQ

answer is D.

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Detailed Solution

In ΔPQR,

∠P + ∠Q + ∠R = 180^o [Angle sum property of a triangle]

⇒ 70^o + 75^o + ∠R = 180^o

⇒ ∠R = 180^o − 145^o = 35^o

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So, in ΔPQR,

∠P = 70^o, ∠Q = 75^o, and ∠R = 35^o

∴ ∠Q > ∠P > ∠R

We know that in a triangle, the side opposite to the larger angle is longer.

Therefore, PR > QR > PQ

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