JEE PYQ: Properties Of Triangle Question 3
Question 3 - 2019 (08 Apr Shift 2)
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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(1) $5 : 9 : 13$
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(2) $4 : 5 : 6$
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(3) $3 : 4 : 5$
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(4) $5 : 6 : 7$
Show Answer
Answer: (2) $4 : 5 : 6$
Solution
Let the sides be $a > b > c$ with $A = 2C$ and sides in A.P. After applying Napier’s analogy and solving: $\cos C = \frac{3}{4}$, yielding ratio $\sin A : \sin B : \sin C = 6 : 5 : 4$.
BETA
