Tick the correct answer and justify:ABC and BDE are two equilateral triangles such that D is the mid point of BC Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
(A) 2:3  (B) 4:9 (C) 81:16 (D) 16:81

Explanation

Please refer to video for the figure.

`Delta BCA` and `DeltaBDE` will be similar triangle as they are equilateral and all their angles will be `60^@`.
Also, we know for similar triangles,

`(Area(T1))/(Area(T2)) = (Sides(T1)^2)/(Sides(T2)^2)`


As, `Delta BCA` and `DeltaBDE` are similar.

`(Area(Delta BCA))/(Area(Delta BDE)) = (BC^2)/(BD^2)=(2BD)^2/(BD^2) =4/1`



...