JEE Main 2019MathematicsProperties of TrianglesHardMCQ

JEE Main 2019 — Properties of Triangles Question with Solution

JEE Main 2019 (08 Apr Shift 2)

Question

If the lengths of the sides of a triangle are in A.P and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

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Show full solutionCorrect option: D
Correct answer
D4:5:6

Step-by-step explanation

Let a<b<c are three sides and θ is the smallest angle. Hence three angles are θ, π-3θ, 2θ
Given, 2b=a+c⇒2sin⁡B=sin⁡A+sin⁡C (using sine rule)
⇒2sin 3θ=sin θ+sin 2θ
⇒23sin θ-4sin3θ=sin θ1+2cos θ
⇒6-81-cos2θ=1+2cos θ
⇒cos θ=34, -12 ( -12 is rejected since θ is acute)
∴ a:b:c=sinA:sin B:sin C=sin θ:sin 3θ:  sin 2θ
=1:3-4 sin2θ:2cos θ=1:4cos2θ-1:2 cos θ
=4:5:6

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About this question

This is a previous-year question from JEE Main 2019, covering the Properties of Triangles chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.