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 :
\[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}=\,\,110\,\,cm\,\,and\,\,{{n}_{1}}{{l}_{1}}\,\,=\,\,{{n}_{2}}{{l}_{2}}\,\,=\,\,{{n}_{3}}{{l}_{3}}\] \[{{n}_{1}}:{{n}_{2}}:{{n}_{3}}\,\,:\,\,:\,\,1:2:3\] \[\because \,\,\,\,\,\frac{{{n}_{1}}}{{{n}_{2}}}-\frac{1}{2}=\frac{{{l}_{2}}}{{{l}_{1}}}\,\,=\,\,\,\,\Rightarrow \,\,{{l}_{2}}\,\,=\,\,\frac{{{l}_{1}}}{2}\,\,and\] \[\frac{{{n}_{1}}}{{{n}_{3}}}-\frac{1}{3}=\frac{{{l}_{3}}}{{{l}_{1}}}\,\,=\,\,\,\,\Rightarrow \,\,{{l}_{3}}\,\,=\,\,\frac{{{l}_{1}}}{3}\,\,\] \[{{l}_{1}}\,+\,\frac{{{l}_{1}}}{2}\,\,+\,\frac{{{l}_{1}}}{3}\,\,=\,\,\,110\,\] \[so\,\,{{l}_{1}}=60\,\,cm,\,\,{{l}_{2}}=30\,cm,\,\,{{l}_{3}}=20\,cm\]
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