Q7 of 186 Page 211

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


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