có ai giúp mình giải bài này với được k ( mình cần gấp, mình cảm ơn)
-Bài 3: cho tam giác ABC vuông tại A , đường cao AH, biết AH:AC=3:5 và AB=15cm
a, tính HB và HC
b, gọi E, F lần lượt là hình chiếu của H trên AB và AC ; chứng minh AB.AC=EF.BC
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Bài 5:
Xét ΔABC vuông tại A
Áp dụng Pytago ta có:
BC2 = AB2 + AC2
= 242 + 322
⇒ BC = 40
DE là trung trực của BC
⇒ E là trung điểm của BC; DE vuông góc với BC tại E
⇒ EC = BC/2 = 40/2 = 20
Xét ΔCED và ΔCAB có:
∠CED = ∠CAB = 90o
∠C chung
⇒ ΔCED đồng dạng ΔCAB
⇒ CE/CA = ED/AB
⇒ 12/32 = ED/24
⇒ ED = 9
Bài 2:
Ta có: \(\dfrac{BD}{DC}=\dfrac{3}{7}\)
nên \(\dfrac{AB}{AC}=\dfrac{3}{7}\)
hay \(AB=\dfrac{3}{7}AC\)
Áp dụng định lí Pytago vào ΔABC vuông tại A, ta được:
\(BC^2=AB^2+AC^2\)
\(\Leftrightarrow AC^2\cdot\dfrac{9}{49}+AC^2=20^2=400\)
\(\Leftrightarrow AC^2=\dfrac{9800}{29}\)
\(\Leftrightarrow AC=\dfrac{70\sqrt{58}}{29}\left(cm\right)\)
\(\Leftrightarrow AB=\dfrac{3}{7}\cdot AC=\dfrac{30\sqrt{58}}{29}\left(cm\right)\)
Lời giải:
a. Vì $AH:AC=3:5$ nên đặt $AH=3a; AC=5a$ với $a>0$
Ta có: $AH=\frac{2S_{ABC}}{BC}=\frac{AB.AC}{BC}$
$AH^2=\frac{AB^2AC^2}{BC^2}=\frac{AB^2.AC^2}{AB^2+AC^2}$
$(3a)^2=\frac{15^2.(5a)^2}{15^2+(5a)^2}$
$\Leftrightarrow 9a^2=\frac{225a^2}{a^2+9}$
$\Leftrightarrow 9=\frac{225}{a^2+9}$
$\Leftrightarrow 9(a^2+9)=225$
$\Rightarrow a=4$ (cm)
$AH=3a=12$ (cm); $AC=5a=20$ (cm)
Áp dụng định lý Pitago:
$HC=\sqrt{AC^2-AH^2}=\sqrt{20^2-12^2}=16$ (cm)
$HB=\sqrt{AB^2-AH^2}=\sqrt{15^2-12^2}=9$ (cm)
b.
Vì $AEHF$ có 3 góc vuông $\widehat{A}=\widehat{E}=\widehat{F}=90^0$ nên đây là hình chữ nhật
$\Rightarrow EF=AH$
Do đó: $EF.BC=AH.BC=2S_{ABC}=AB.AC$ (đpcm)
Hình vẽ:
![](data:image/png;base64,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)