Toán Lớp 9: Cho tam giác ABC vuông tại A , đường cao AH , AH=12cm, BC=25cm. Tính AB, AC, HC,BH .
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Toán Lớp 9: Cho tam giác ABC vuông tại A , đường cao AH , AH=12cm, BC=25cm. Tính AB, AC, HC,BH .
Comments ( 1 )
AB = 15cm;AC = 20cm;HC = 9cm;HB = 16cm\\
AB = 20cm;AC = 15cm;HC = 16cm;HB = 9cm
\end{array} \right.$
+ )AB.AC = AH.BC = 12.25 = 300\\
\Leftrightarrow AB = \dfrac{{300}}{{AC}}\\
+ )A{B^2} + A{C^2} = B{C^2}\\
\Leftrightarrow {\left( {\dfrac{{300}}{{AC}}} \right)^2} + A{C^2} = {25^2}\\
\Leftrightarrow 90000 + A{C^4} = 625.A{C^2}\\
\Leftrightarrow A{C^4} – 625.A{C^2} + 90000 = 0\\
\Leftrightarrow \left( {A{C^2} – 400} \right)\left( {A{C^2} – 225} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
A{C^2} = 400\\
A{C^2} = 225
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
AC = 20 \Leftrightarrow AB = \dfrac{{300}}{{20}} = 15\\
AC = 15 \Leftrightarrow AB = \dfrac{{300}}{{15}} = 20
\end{array} \right.\\
+ )Khi:AC = 20;AB = 15\\
\Leftrightarrow H{C^2} = A{C^2} – A{H^2} = {15^2} – {12^2} = 81\\
\Leftrightarrow HC = 9\left( {cm} \right)\\
\Leftrightarrow HB = BC – HC = 25 – 9 = 16\left( {cm} \right)\\
+ )Khi:AC = 15;AB = 20\\
\Leftrightarrow HC = 16;HB = 9\\
Vậy\,\left\{ \begin{array}{l}
AB = 15cm;AC = 20cm;HC = 9cm;HB = 16cm\\
AB = 20cm;AC = 15cm;HC = 16cm;HB = 9cm
\end{array} \right.
\end{array}$