In using Pythagoras theorem, we get

AB² + BC² = AC²

9 + BC² = 25

BC = 4 cm

In

∠BAC = ∠CAD (Therefore, AC is bisector of ∠A)

∠B = ∠D = 90^o

∠ABC + ∠BCA + ∠CAB = 180^o

∠CAD + ∠ADC + ∠DCA = 180^o

∠ABC + ∠BCA + ∠CAB = ∠CAD + ∠ADC + ∠DCA

∠BCA = ∠DCA (i)

In

∠CAB = ∠CAD (Therefore, AC is bisector of ∠A)

∠BCA = ∠DCA [From (i)

AC = AC (Common)

By ASA theorem, we have

BC = CD (By c.p.c.t)

CD = 4cm