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Question

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
( 1 mark )
Consider ΔABD and ΔACB:
BAD=CAB ----[common angle]
BDA=CBA ----[90]
By AA similarity criterion,ΔABDΔABC
( 1 mark )
Hence,
Ar(ΔABD)Ar(ΔACB)=(ABAC)2=(12)2=14
i.e., Ar(ΔABD)×4=Ar(ΔACB)Ar(ΔABD)=54=1.25 sq.units
Hence, the area of ΔABD is 1.25 sq.units.
( 1 mark )

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