We know that (a+b+c)2 = a2+b2+c2 + 2(ab + bc + ca) a2 + b2 + c2 = ab + bc + ca (given) (a+b+c)2 = (ab + bc + ca)+ 2(ab + bc + ca) (a+b+c)2 = 3 (ab + bc + ca) (3a)2 = 3(a2+b2+c2) (3a)2 = 3(3a2) 9a2 = 9a2 It is possible only when the three sides of a triangle is equal. So, the triangle is an equilateral triangle.