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Question

In a right triangle Δ ABC, right angled at B, BD is a perpendicular dropped onto the hypotenuse AC.

If AC = 2AB, find the area of Δ ABD, given, area of Δ ABC = 5 sq units.


A

0.5 sq. units

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B

1 sq. unit

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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(Δ ABC)=5 sq.units

In Δ ABD and Δ ABC,

BAD=BAC
(common angle in both the triangles)

BDA=ABC= 90

So, ΔABDΔACB (by AA similarity criterion)

Ar (ΔABD)Ar (ΔACB)=(ABAC)2=(12)2=14

Ar (ΔABD)=Ar(ΔACB)4

Ar(ΔABD)=54=1.25 sq.units

Hence, the area of Δ ABD is 1.25 sq.units.


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