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