In a right triangle △ABC right angled at B, BD is a perpendicular, dropped onto the hypotenuse. If AC=2AB and area of △ABC =5 sq. units, what is the area of △ABD?
1.25 sq. units
Given, ABAC=12 and Ar△ABC=5 sq.units
Consider △ABD and △ABC
∠BAD=∠BAC [commom angle]
∠BDA=∠ABC [90∘]
By AA similarity criterion, △ABD∼△ABC
Hence, Ar(△ABD)Ar(△ABC)=(ABAC)2=(12)2=14
i.e., Ar△ABD)×4=Ar(△ABC)
⇒Ar(△ABD)=54=1.25 sq.units
Hence, the area of △ABD is 1.25 sq. units