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
∴ABCADE [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