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

##### 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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