b) Tính độ dài các cạnh của tam giác ABC.

b) Ta có m_a = 15, m_b = 18, m_c = 27.

$\Rightarrow \left\{\begin{array}{l}{b}^2+c^2=2m_a^2+\frac{a^2}{2}\\ a^2+c^2=2m_b^2+\frac{b^2}{2}\\ a^2+b^2=2m_c^2+\frac{c^2}{2}\end{array}\right.$

$\Rightarrow \left\{\begin{array}{l}{a}^2+b^2+c^2=\frac{4}{3}\left(m_a^2+m_b^2+m_c^2\right)=1704\\ b^2-a^2=\frac{4}{3}\left(m_a^2-m_b^2\right)=-132\\ b^2-c^2=\frac{4}{3}\left(m_c^2-m_b^2\right)=540\end{array}\right.$

$\Rightarrow \left\{\begin{array}{l}{a}^2=836\\ b^2=704\\ c^2=164\end{array}\right.$.

$\Rightarrow \left\{\begin{array}{l}a=2\sqrt{209}\\ b=8\sqrt{11}\\ c=2\sqrt{41}\end{array}\right.$

Vậy $a=BC=2\sqrt{209};b=AC=8\sqrt{11};c=AB=2\sqrt{41}$