B = 45 degrees

DE⊥EB

△DEB

This is an isosceles right triangle.

AD is the angular bisector of △ABC.

So DE=CD

DB= root number 2 *DE

BC=( 1+ root number 2)DE

AB= radical number 2 *BC=(2+ radical number 2)*DE

△DEB perimeter =DE+EB+DB=(2+ radical number 2)*DE=AB

=6 cm