ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is

(A) 2 : 1

(B) 1 : 2

(C) 4 : 1

(D) 1 : 4

Asked by Pragya Singh | 1 year ago |  43

1 Answer

Solution :-

Right answer is (C)  4 : 1

GivenΔABC and ΔBDE are two equilateral triangle. D is the midpoint of BC.

 BD = DC = \( \dfrac{1}{2}\)BC

Let each side of triangle is 2a.

As, ΔABC ~ ΔBDE

\( \dfrac{Area(ΔABC)}{Area(ΔBDE)}\) = \( \dfrac{AB^2}{BD^2}\)

= \( \dfrac{(2a)^2}{(a)^2}\) = \( \dfrac{4a^2}{a^2}\)\( \dfrac{4}{1}\) = 4:1

Answered by Abhisek | 1 year ago

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