a. Gọi chiều cao tương ứng BC và AH

\Rightarrow AH=\dfrac{2}{3}BC⇒AH=32​BC

Ta có S_{ABC}=\dfrac{1}{2}\times AH\times BC=\dfrac{1}{2}\times\dfrac{2}{3}BC\times BCSABC​=21​×AH×BC=21​×32​BC×BC

\Rightarrow675=\dfrac{1}{3}\times BC^2\\ \Rightarrow BC^2=2025\\ \Rightarrow BC=45\left(cm\right)\\ \Rightarrow AH=\dfrac{2}{3}\times45=30\left(cm\right)⇒675=31​×BC2⇒BC2=2025⇒BC=45(cm)⇒AH=32​×45=30(cm)