50 followers Problem!!

A right angled triangle ABC was given in which angle C is 90 degrees and $BC = 4$ . $D$ is a point on $BC$ such that $AD = 3$ . Given that the perimeter of triangle ABD is equal to the perimeter of triangle ADC. Find:-

$BD:DC.$

This ratio can be expressed as a:b where a and b are co-prime numbers. What is $a + b$ ?