A) 2b
B) 2c
C) 3b
D) 3a
Correct Answer: C
Solution :
\[\because \] \[A:B:C=3:5:4\] Þ \[A+B+C=12x={{180}^{o}}\,\,\Rightarrow \,\,x={{15}^{o}}\] \[\therefore \] \[A={{45}^{o}},\,B={{75}^{o}},\,C={{60}^{o}}\] \[\frac{a}{\sin {{45}^{o}}}=\frac{b}{\sin {{75}^{o}}}=\frac{c}{\sin {{60}^{o}}}=K\] (say) \[\therefore \,a=\frac{1}{\sqrt{2}}K,\,\,\,\,b=\frac{\sqrt{3}+1}{2\sqrt{2}}K,\,\,\,\,c=\frac{\sqrt{3}}{2}K\] \[\therefore \,\,a+b+c\sqrt{2}=3b.\]
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