Cho tam giác ABC vuông tại A đường cao AH. Tính chu vi của tam giác ABC biết AH= 14cm, HB/HC = 1/4
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: AB/AC=5/7
=>HB/HC=(AB/AC)^2=25/49
=>HB/25=HC/49=k
=>HB=25k; HC=49k
ΔABC vuông tại A có AH là đường cao
nên AH^2=HB*HC
=>1225k^2=15^2=225
=>k^2=9/49
=>k=3/7
=>HB=75/7cm; HC=21(cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
Áp dụng hệ thức lượng trong tam giác vuông có:
\(AH^2=BH.BC\Leftrightarrow BH.BC=196\)
\(\dfrac{HB}{HC}=\dfrac{1}{4}\Leftrightarrow HB=\dfrac{HC}{4}\)
\(\Rightarrow HB.HC=\dfrac{HC^2}{4}=196\Leftrightarrow HC=28\)\(\Rightarrow HB=7\)
\(\Rightarrow BC=HB+HC=28+7=35\) (cm)
Vậy BC=35cm.
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(\dfrac{HB}{HC}=\dfrac{1}{4}\Rightarrow4HB=HC\)
Xét tam giác ABC vuông tại A có đường cao AH:
\(AH^2=BH.HC\)( hệ thức lượng trong tam vuông)
\(\Rightarrow14^2=HB.4HB\Rightarrow HB=7\left(cm\right)\Rightarrow HC=4HB=28\left(cm\right)\Rightarrow BC=HB+HC=35\left(cm\right)\)Xem tam giác ABC vuông tại A có đường cao AH:
\(\left\{{}\begin{matrix}AB^2=HB.BC\\AC^2=HC.BC\end{matrix}\right.\)(Hệ thức lượng trong tam giác vuông)
\(\Rightarrow\left\{{}\begin{matrix}AB^2=7.35\\AC^2=28.35\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}AB=7\sqrt{5}\\AC=14\sqrt{5}\end{matrix}\right.\)
Ta có: \(P_{ABC}=AB+AC+BC=7\sqrt{5}+14\sqrt{5}+35=35+21\sqrt{5}\left(cm\right)\)
Ta có: \(\dfrac{HB}{HC}=\dfrac{1}{4}\)
\(\Leftrightarrow HC=4HB\)
Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(AH^2=HB\cdot HC\)
\(\Leftrightarrow4\cdot HB^2=14^2=196\)
\(\Leftrightarrow HB^2=49\)
\(\Leftrightarrow HB=7\left(cm\right)\)
\(\Leftrightarrow HC=28\left(cm\right)\)
Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(\left\{{}\begin{matrix}AB^2=HB\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB^2=7\cdot35=245\\AC^2=28\cdot35=980\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB=7\sqrt{5}\left(cm\right)\\AC=14\sqrt{5}\left(cm\right)\end{matrix}\right.\)
Chu vi tam giác ABC là:
\(C_{ABC}=AB+AC+BC=21\sqrt{5}+35\left(cm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(HB:HC=2:3\Rightarrow\dfrac{HB}{2}=\dfrac{HC}{3}\Rightarrow HB=\dfrac{2}{3}HC\)
Áp dụng HTL:
\(AH^2=BH\cdot HC\Rightarrow24^2=\dfrac{2}{3}HC^2\Rightarrow HC^2=576\cdot\dfrac{3}{2}=864\\ \Rightarrow HC=12\sqrt{6}\left(cm\right)\\ \Rightarrow HB=\dfrac{2}{3}\cdot12\sqrt{6}=8\sqrt{6}\left(cm\right)\\ \Rightarrow BC=HB+HC=20\sqrt{6}\left(cm\right)\\ \Rightarrow S_{ABC}=\dfrac{1}{2}AH\cdot BC=\dfrac{1}{2}\cdot24\cdot20\sqrt{6}=240\sqrt{6}\left(cm^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Để tính chu vi của tam giác ABC, ta cần biết độ dài các cạnh của tam giác. Tuy nhiên, từ thông tin đã cho, chúng ta chỉ biết đường cao AH có độ dài là 14cm và tỉ lệ HB/HC là 1/4. Để tính chu vi, chúng ta cần thêm thông tin về độ dài các cạnh khác của tam giác.
ΔABC vuông tại A có AH là đường cao
nên AH^2=HB*HC
=>HB*HB*4=14^2=196
=>HB=7(cm)
HC=7*4=28cm
BC=7+28=35cm
\(AB=\sqrt{7\cdot35}=7\sqrt{5}\left(cm\right)\)
\(AC=\sqrt{28\cdot35}=14\sqrt{5}\left(cm\right)\)
\(C_{ABC}=7\sqrt{5}+14\sqrt{5}+35=21\sqrt{5}+35\left(cm\right)\)
Lời giải:
Vì $HB:HC=1:4$ nên đặt $HB=a; HC=4a$ với $a>0$
Áp dụng HTL trong tam giác vuông:
$AH^2=BH.CH$
$14^2=a.4a$
$4a^2=196$
$a^2=49\Rightarrow a=7$ (do $a>0$)
Khi đó:
$BH=a=7$ (cm); $CH=4a=28$ (cm)
$BC=BH+CH=7+28=35$ (cm)
$AB=\sqrt{AH^2+BH^2}=\sqrt{14^2+7^2}=7\sqrt{5}$ (cm)
$AC=\sqrt{AH^2+CH^2}=\sqrt{14^2+28^2}=14\sqrt{5}$ (cm)
Chu vi tam giác $ABC$:
$P=AB+BC+AC=7\sqrt{5}+14\sqrt{5}+35=21\sqrt{5}+35$ (cm)
Hình vẽ:
![](data:image/png;base64,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)