SOLUTION: Let {{{a}}}, {{{b}}} and {{{c}}} be the sides of a triangle. If {{{a^2 + b^2 + c^2 = ab + bc + ca}}}, find the type of triangle it is.

Algebra ->  Triangles -> SOLUTION: Let {{{a}}}, {{{b}}} and {{{c}}} be the sides of a triangle. If {{{a^2 + b^2 + c^2 = ab + bc + ca}}}, find the type of triangle it is.      Log On

If   = ab + ac + bc,  then


 = 2*(ab + ac + bc),   or,  equivalently,


 = 0,


which implies  a = b,  a = c  and  b = c.


Hence, the triangle is  EQUILATERAL.