question_answer

\[\left( {{x}_{i}},{{y}_{i}} \right)\]are vertices of a equilateral triangle ABC such that \[{{\left( {{x}_{1}}-2 \right)}^{2}}+{{\left( {{y}_{1}}-3 \right)}^{2}}={{\left( {{x}_{2}}-2 \right)}^{2}}+{{\left( {{y}_{2}}-3 \right)}^{2}}\] \[={{\left( {{x}_{3}}-2 \right)}^{2}}+{{\left( {{y}_{3}}-3 \right)}^{2}}\].Then \[2\left( {{x}_{1}}+{{x}_{2}}+{{x}_{3}} \right)+3\left( {{y}_{1}}+{{y}_{2}}+{{y}_{3}} \right)=\]

Answer:

39.00