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# Tick the correct answer and justify: ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is

Q8   Tick the correct answer and justify :
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of
the areas of triangles ABC and BDE is

(A) 2 : 1

(B) 1 : 2

(C) 4 : 1

(D) 1 : 4

Views

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

All angles of the triangle are $60 \degree$.

$\triangle$ABC $\sim \triangle$ BDE    (By AAA)

Let AB=BC=CA = x

then   EB=BD=ED=$\frac{x}{2}$

$\frac{ar(\triangle ABC)}{ar(\triangle BDE)}=(\frac{x}{\frac{x}{2}})^2=\frac{4}{1}$

Option C is correct.

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