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.
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, ΔABD∼ΔACB (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.