Question
In a $\triangle\text{ABC},$ if $3\angle\text{A}=4\angle\text{B}=6\angle\text{C}$ then A : B : C =?
✓
Answer
- 4 : 3 : 2
Solution:
Given that $3\angle\text{A}=4\angle\text{B}=6\angle\text{C}=\text{k}.$
$\Rightarrow\angle\text{A}=\frac{\text{k}}{3},\angle\text{B}=\frac{\text{k}}{4}\text{ and}\ \angle\text{C}=\frac{\text{k}}{6}$
$\Rightarrow\text{A}:\text{B}:\text{C}=\frac{\text{k}}{3}:\frac{\text{k}}{4}:\frac{\text{k}}{6}$
$\Rightarrow\text{A}:\text{B}:\text{C}=\frac{1}{3}:\frac{1}{4}:\frac{1}{3}$
The LCM of 3, 4 and 6 is 12.
Multiply by 12 throughout.
⇒ A : B : C = 4 : 3 : 2
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