Question

$Ina\Delta ABC,if3\angle A=4\angle B=6\angle CthenA:B:C=?$

(a) 3:4:6 (b) 4:3:2 (c) 2:3:4 (d) 6:4:3

Answer 1

ANSWER:
LCM of 3, 4 and 6 = 12
3 $\angle A=4\angle B=6\angle C$
(Given)
Dividing throughout by 12, we get
3 $\angle A/12=4\angle /B12=6\angle C/12\Rightarrow \angle A/4=\angle B/3=\angle C/2$
Let $\angle A/4=\angle B/3=\angle C/2$=k, where k is some constant
Then, $\angle A=4k,\angle B=3k,\angle C=2k$
∴ $\angle A:\angle B:\angle C$ = 4 k : 3 k : 2 k = 4 : 3 : 2
Hence, the correct answer is option (b).