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