Let a, b and c be the sides of a triangle ABC.

Question :Is the triangle equilateral?

Statement - I :a² + b²+ c²= (ab + bc + ca)

Statement - II :3a² + 3b² + 4c² = 2ab + 4bc + 4ca

Correct option is B

Solution:

Statement 1: 

$$a^2 + b^2 + c^2 = (ab + bc + ca)\\ \\If \ a^2 + b^2 + c^2 = (ab + bc + ca)\ than\ a = b = c$$​​

The triangle is equilateral, hence statement 1 alone is sufficient to answer the question.

Statement 2:

3a² + 3b² + 4c² = 2ab + 4bc + 4ca

This can be rearranged to:
3a² + 3b² + 4c² - 2ab - 4bc - 4ca = 0

Next, we group the terms:
(a² + b² - 2ab) + (2b² + 2c² - 4bc) + (2c² + 2a² - 4ca) = 0

This simplifies to:
(a - b)² + (√2b - √2c)² + (√2c - √2a)² = 0

a = b and b = c

Hence both statements alone are sufficient to answer the question.

∴ The correct answer is option b.