In a ΔPQR,∠P : ∠Q : ∠R = 3 ∶ 4 ∶ 8. The shortest side and the longest side of the triangle, respectively, are:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. QR and PQ.
Given that
In a ΔPQR, ∠P: ∠Q: ∠R = 3∶ 4∶ 8
As we know,
⇒ ∠P + ∠Q + ∠R = 180º
⇒ 3x + 4x + 8x = 180º
⇒ 15x = 180º
⇒ x = 12º
⇒ ∠P = 3x = 12 × 3 = 36º
⇒ ∠Q = 4x = 12 × 4 = 48º
⇒ ∠R = 8x = 12 × 8 = 96º
As we know, the longest side is opposite to the largest angle and the smallest side is opposite to the smallest angle of a triangle.
Hence, PQ is the longest side and QR is the smallest side of the triangle