Simple Question on Triangles...

Question

What times the sum of the squares of the sides of a triangle is equal to the sum of the squares of the medians of the triangle.

Answer 1

Hint:

$\Large 2\cdot m_a^2+\frac{a^2}{2}=b^2+c^2$

$\Large 2\cdot m_b^2+\frac{b^2}{2}=c^2+a^2$

$\Large 2\cdot m_c^2+\frac{c^2}{2}=a^2+b^2$