Cho tam giác có độ dài ba cạnh lần lượt là \(1\), \(2\), \(\sqrt{5}\). Độ dài đường cao ứng với cạnh lớn nhất bằng
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Nửa chu vi của tam giác là: \(p=\frac{1+2+\sqrt{5}}{2}\).
Diện tích tam giác là: \(S=\sqrt{p\left( p-1 \right)\left( p-2 \right)\left( p-\sqrt{5} \right)}=1\).
Đặt \(a=1\), \(b=2\), \(c=\sqrt{5}\).
Độ dài đường cao ứng với cạnh lớn nhất là: \({{h}_{c}}=\frac{2S}{c}=\frac{2.1}{\sqrt{5}}=\frac{2\sqrt{5}}{5}\).
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