\(\Delta ABC\perp\) tại A ; \(AH\perp BC\) . Áp dụng HTL ; ta có :
\(\dfrac{AB^2}{AC^2}=\dfrac{BH.BC}{CH.BC}=\dfrac{BH}{CH}\Rightarrow\left(\dfrac{5}{7}\right)^2=\dfrac{BH}{CH}\) \(\Rightarrow\dfrac{BH}{CH}=\dfrac{25}{49}\) \(\Rightarrow\dfrac{x}{y}=\dfrac{25}{49}\)
\(BH.CH=AH^2=15^2\Rightarrow xy=225\)
Ta có : \(\left\{{}\begin{matrix}49x=25y\\xy=225\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{25}{49}y\\\dfrac{25}{49}y^2=225\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{25}{49}y\\y^2=441\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{25}{49}y\\y=21\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{75}{7}\\y=21\end{matrix}\right.\) (cm)
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