Question 151

# If a,b,c are the sides of a triangle, and $$a^2 + b^2 +c^2 = bc + ca + ab$$, then the triangle is:

Solution

$$(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) => 3(a^2 + b^2 + c^2)$$

This is possible only if a = b = c.

So, the triangle is an equilateral triangle.