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Question

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?


A

0.5 sq. units

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B

1 sq. units

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C

1.25 sq. units

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D

5 sq. units

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Solution

The correct option is C

1.25 sq. units



Given, ABAC=12 and ArABC=5 sq.units
Consider ABD and ABC
BAD=BAC [commom angle]
BDA=ABC [90]
By AA similarity criterion, ABDABC
Hence, Ar(ABD)Ar(ABC)=(ABAC)2=(12)2=14
i.e., ArABD)×4=Ar(ABC)
Ar(ABD)=54=1.25 sq.units
Hence, the area of ABD is 1.25 sq. units


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