Question

In ∆ABC, if 3∠A = 4∠B = 6∠C then A : B : C = ?
(a) 3 : 4 : 6
(b) 4 : 3 : 2
(c) 2 : 3 : 4
(d) 6 : 4 : 3

Answer 1

LCM of 3, 4 and 6 = 12

3∠A = 4∠B = 6∠C (Given)

Dividing throughout by 12, we get

$\frac{3\angle \mathrm{A}}{12}=\frac{4\angle \mathrm{B}}{12}=\frac{6\angle \mathrm{C}}{12}$

$\Rightarrow \frac{\angle \mathrm{A}}{4}=\frac{\angle \mathrm{B}}{3}=\frac{\angle \mathrm{C}}{2}$

Let $\frac{\angle \mathrm{A}}{4}=\frac{\angle \mathrm{B}}{3}=\frac{\angle \mathrm{C}}{2}=k$, where k is some constant

Then, ∠A = 4k, ∠B = 3k, ∠C = 2k

∴ ∠A : ∠B : ∠C = 4k : 3k : 2k = 4 : 3 : 2

Hence, the correct answer is option (b).