CAT 2024 Geometry & Mensuration — Previous Year Question

$A B C D$ is a trapezium in which $A B$ is parallel to $C D$ . The sides $A D$ and $B C$ when extended, intersect at point $E$ . If $A B=2 \mathrm{~cm}, C D=1 \mathrm{~cm}$ , and perimeter of $A B C D$ is 6 cm , then the perimeter, in cm , of $\triangle A E B$ is