We have,

AB=AC=25cm

BC=14cm

In ⊿ ACD and ⊿ ABD

∠ADB=∠ADB=90

AB=AC=25cm

AD=AD (Common)

⊿ ABD≅∠ACD

∴BD=CD=7cm (By c.p.c.t)

In ⊿ACD

AB²=AD²+BD²

25²=AD²+72

625=AD²+49

AD²=625-49

AD²=576

AD=

AD=24 cm