Mathematics - Properties of Triangle Question with Solution | TestHub

Let $m_b$ be the length of the median from vertex B to side AC. The formula for the length of a median $m_b$ is $m_b^2=\frac{2a^2+2c^2-b^2}{4}$. Substituting the given side lengths $a=7,b=8,c=9$:$m_b^2=\frac{2(7^2)+2(9^2)-8^2}{4}=\frac{2(49)+2(81)-64}{4}$.$m_b^2=\frac{98+162-64}{4}=\frac{260-64}{4}=\frac{196}{4}=49$. Therefore, $m_b=\sqrt{49}=7$.