Hỏi \(x=?\) và \(y=?\) trong hình vẽ sau:
\(x=\dfrac{\sqrt{10}}{5}cm;y=\dfrac{9\sqrt{10}}{5}cm.\) \(x=\dfrac{2\sqrt{10}}{5}cm;y=\dfrac{3\sqrt{10}}{5}cm.\) \(x=\dfrac{4\sqrt{10}}{5}cm;y=\dfrac{6\sqrt{10}}{5}cm.\) \(x=\dfrac{3\sqrt{10}}{5}cm;y=\dfrac{7\sqrt{10}}{5}cm.\) Hướng dẫn giải:
\(BC=\sqrt{2^2+6^2}=\sqrt{40}=2\sqrt{10}\)(cm).
\(AB^2=BH.BC\Leftrightarrow2^2=BH.2\sqrt{10}\)
\(\Leftrightarrow BH=\dfrac{2^2}{2\sqrt{10}}=\dfrac{\sqrt{10}}{5}cm\).
\(CH=BC-BH=2\sqrt{10}-\dfrac{\sqrt{10}}{5}=\dfrac{9\sqrt{10}}{5}cm\).
Vậy \(x=\dfrac{\sqrt{10}}{5}cm;y=\dfrac{9\sqrt{10}}{5}cm.\)
