If the area of a $\triangle A B C$ is $4 \sqrt{5}$ sq units. Length of the side $C A$ is 6 units and $\tan \frac{B}{2}=\frac{\sqrt{5}}{4}$, then its smallest side is of length

In a $\triangle A B C$ if $r_1=2 r_2=3 r_3$, then $a: b$ is

$$ \text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to } $$