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In the given figure, ∠CAB = 90° and AD ⊥ BC. Show that ΔBDA ~ ΔBAC. If AC = 75 cm, AB = 1 cm and BC = 1.25 cm, find AD.

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Given: ∠CAB =90° and AD⊥ BC

and AC = 75 cm, AB = 1 cm and BC = 1.25 cm

Now, In ΔADB and ΔCAB

∠ADB = ∠CAB [each 90°]

∠ABD = ∠CBA [common angle]

∴ ΔADB ~ ΔCAB [by AA similarity]

Since the triangles are similar, hence corresponding sides are in proportional.

⇒ AD = 60 cm

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