A diagonal of rhombus \( \mathrm{ABCD} \) is member of both the families of lines \( (x+y-1)+\la...

A diagonal of rhombus \( \mathrm{ABCD} \) is member of both the families of lines \( (x+y-1)+\lambda_{1}(2 x+3 y-2)=0 \) and \( (x-y+2)+\lambda_{2}(2 x-3 y+5)=0 \) where \( \lambda_{1}, \lambda_{2} \in R \) and one of the vertex of the rhombus is \( (3,2) \).
If area of the rhombus is \( 12 \sqrt{5} \) square units, then find the length of longer diagonal of the rhombus.