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

Given that, ∠CAB = 90°

AC = 75 cm

AB = 1 m

BC = 1.25 m

To show that, ∆BDA ∼ ∆BAC

In the diagram, we can see

∠BDA = ∠BAC = 90°

∠DBA = ∠CBA [They are common angles]

So by AA-similarity theorem,

∆BDA ∼ ∆BAC

Thus, now since ∆BDA ∼ ∆BAC, we can write as

⇒ [∵ AC = 75 cm, AB = 1 m = 100 cm & BC = 1.25 m = 125 cm]

⇒

⇒ AD = 60 cm

Hence, AD = 60 cm or 0.6 m