A) 20 cm; 30 cm; 60 cm
B) 60 cm; 30 cm; 20 cm
C) 60 cm; 20 cm; 30 cm
D) 30 cm; 60 cm; 20 cm
Correct Answer: B
Solution :
Given,\[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}=110\,\,cm\] and \[{{n}_{1}}{{l}_{1}}={{n}_{2}}{{l}_{2}}={{n}_{3}}{{l}_{3}}\] \[{{n}_{1}}:{{n}_{2}}:{{n}_{3}}::1:2:3\] \[\because \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{1}{2}=\frac{{{l}_{2}}}{{{l}_{1}}}\] \[\Rightarrow \] \[{{l}_{2}}=\frac{{{l}_{1}}}{2}\] and \[\frac{{{n}_{1}}}{{{n}_{3}}}=\frac{1}{3}=\frac{{{l}_{3}}}{{{l}_{1}}}\] \[\Rightarrow \] \[{{l}_{3}}=\frac{{{l}_{1}}}{3}\] \[\therefore \] \[{{l}_{1}}+\frac{{{l}_{1}}}{2}+\frac{{{l}_{1}}}{3}=110\] So,\[{{l}_{1}}=60\,\,cm,\,\,{{l}_{2}}=30\,\,cm,\,\,{{l}_{3}}=20\,\,cm\]
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