√3a=2csinA
a>c
a/c=2sinA/√3
根据正弦定理
a/sinA=c/sinC
a/c=sinA/sinC
2sinA/√3=sinA/sinC
2/√3=1/sinC
sinC=√3/2
C=60°
S=1/2*absinC
3√3/2=1/2*ab√3/2
3=1/2*ab
ab=6
cosC=(a^2+b^2-c^2)/2ab
1/2=(a^2+b^2-√7^2)/2*6
a^2+b^2-7=6
a^2+b^2=13
a^2+b^2+2ab-2ab=13
(a+b)^2-2*6=13
(a+b)^2=25
a+b=5