AD is and altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area (
) : Area (
) = 3 : 4.
We have,
ABC is an equilateral triangle
AB=BC=AC=2X
∵ AD⊥BC then BD=DC=x
In 
ADB
AB2=(2x)2-(x)2=3x2
AD=
cm
ABC and 
ADE both are equilateral triangles
∴
ABC
ADE [By AA similarity]
By area of similar triangle theorem
Area(
) =AD2 Area (
) AB2
Area(
) Area (
)=(
)2/4x2
Area(
) Area (
) =3/4
Area(
)
Area (
) =3:4
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