Give: ABC and BDE are two equilateral triangles
Since, D is the midpoint of BC and BDE is also an equilateral triangle.
Hence, E is also the midpoint of AB.
Now, D and E are the midpoint of BC and AB.
In a triangle, the line segment that joins midpoint of the two sides of a triangle is parallel to the third side and is half of it.
DE || CA and DE = 1/2 CA
Now, in ∆ABC and ∆EBD
∠BED = ∠BAC
∠B = ∠B
By AA-similarity criterion
∆ABC ~ ∆EBD
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
Hence, the correct answer is option (d).
