What is the distance between points a and b?

answer: sorry i can't you.

step-by-step explanation:

it is given that, b ≅ bc and ad ≅ cd  

we need bd perpendicular to ac, then only we can say   triangles axb and cxb are congruent using the hl theorem.

if bd perpendicular to ac, means that ab and cb are the hypotenuse of triangles axb and cxb respectively.

from the given information abcd is a square

if bd and ac bisect each other then ax = cx

then only we can   immediately possible to prove that triangles axd and cxd are congruent by sss congruence theorem.