Mathematics - Properties of Triangle Question with Solution | TestHub

The length of the median $m_c$ to side $c$ is given by the formula $m_c^2=\frac{2a^2+2b^2-c^2}{4}$. Substituting the given side lengths: $m_c^2=\frac{2(5^2)+2(6^2)-7^2}{4}=\frac{2(25)+2(36)-49}{4}=\frac{50+72-49}{4}=\frac{122-49}{4}=\frac{73}{4}$. Thus, $m_c=\sqrt{73}/2$.