By the law of sine, we have $$\frac{a}{\sin{A}} = \frac{b}{\sin{B}} = \frac{c}{\sin{C}}=2R$$ Hence:$$\frac{a}{\sin{A}} = \frac{b}{\sin{B}} = \frac{c}{\sin{C}} = \frac{a+b+c}{\sin{A}+\sin{B}+\sin{C}}=2R = \boxed{4}$$ Note: The last step utilizes the fact that if $\frac{m}{n}=\frac{x}{y}$, then $\frac{m}{n}=\frac{x}{y}=\frac{m+x}{n+y}$