Tick the correct answer and justify:ABC and BDE are two equilateral tr – InterviewSolution

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1.	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
Answer» 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` (ii) Similarly, ratio of areas of these two triangles will be, `4^2/9^2 = 16/81`.

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