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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

Answers (1)
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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.

\triangleABC \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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