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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 Ar△ABC=5 sq.units Consider △ABD and △ABC ∠BAD=∠BAC [commom angle] ∠BDA=∠ABC [90∘] By AA similarity criterion, △ABD∼△ACB Hence, Ar(△ABD)Ar(△ACB)=(ABAC)2=(12)2=14 i.e., Ar(△ABD)=14×Ar(△ACB) ⇒Ar(△ABD)=54=1.25 sq.units Hence, the area of △ABD is 1.25 sq. units

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