A diagonal of rhombus ABCD is member of both the families of lines (x+y−1)+λ1(2x+3y−2)=0 and (x−y+2)+λ2(2x−3y+5)=0 where λ1 and λ2∈R and one of the vertex of rhombus is (3,2). If area of the rhombus is 12√5 square units, then the length of the longer diagonal of the rhombus is

A diagonal of rhombus ABCD is member of both the families of lines (x

1.	A diagonal of rhombus ABCD is member of both the families of lines (x+y−1)+λ1(2x+3y−2)=0 and (x−y+2)+λ2(2x−3y+5)=0 where λ1 and λ2∈R and one of the vertex of rhombus is (3,2). If area of the rhombus is 12√5 square units, then the length of the longer diagonal of the rhombus is
Answer» A diagonal of rhombus $A B C D$ is member of both the families of lines $(x + y - 1) + λ_{1} (2 x + 3 y - 2) = 0$ and $(x - y + 2) + λ_{2} (2 x - 3 y + 5) = 0$ where $λ_{1}$ and $λ_{2} \in R$ and one of the vertex of rhombus is $(3, 2)$ . If area of the rhombus is $12 \sqrt{5}$ square units, then the length of the longer diagonal of the rhombus is