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The given figure shows ΔPQR whose side PR is extended to point S.
How can the sides PQ, QR, PR of ΔPQR be arranged in ascending order?

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PQ < QR < PR

PR < QR < PQ

QR < PR < PQ

PQ < PR < QR

answer is A.

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Detailed Solution

In ΔPQR, applying exterior angle property of triangles:

∠QRS = ∠RPQ + ∠PQR

⇒ 136° = 67° + ∠PQR

⇒ ∠PQR = 69°

Now, applying angle sum property of triangles in ΔPQR:

∠RPQ + ∠PQR + ∠PRQ = 180°

⇒ 67° + 69° + ∠PRQ = 180°

⇒ ∠PRQ = 44°

It can be observed that: ∠PQR > ∠RPQ > ∠PRQ

It is known that in any triangle, the side opposite to the larger angle is longer.

∴ PR > QR > PQ

Thus, the sides PQ, QR, PR of ΔPQR can be arranged in ascending order as PQ < QR < PR.

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