In a right ΔABC with right angle at B, BD is a perpendicular dropped onto the hypotenuse. If AC = 2AB, what is the area of ΔABD?
Note: Area of ΔABC = 5 sq units
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Solution
Given,ABAC=12 and Ar(Δ ABC) = 5 sq.units
Consider ΔABD and ΔACB: ∠BAD=∠CAB ----[common angle] ∠BDA=∠CBA ----[90∘]
By AA similarity criterion,ΔABD∼ΔABC
Hence, Ar(ΔABD)Ar(ΔACB)=(ABAC)2=(12)2=14
i.e., Ar(ΔABD)×4=Ar(ΔACB)⇒Ar(ΔABD)=54=1.25sq.units
Hence, the area of ΔABD is 1.25 sq.units.