3:

Đặt HB=x; HC=y

Theo đề, ta có: x+y=289 và xy=120^2=14400

=>x,y là các nghiệm của phương trình:

a^2-289a+14400=0

=>a=225 hoặc a=64

=>(x,y)=(225;64) và (x,y)=(64;225)

TH1: BH=225cm; CH=64cm

=>\(AB=\sqrt{225\cdot289}=15\cdot17=255\left(cm\right)\) và \(AC=\sqrt{64\cdot289}=7\cdot17=119\left(cm\right)\)

TH2: BH=64cm; CH=225cm

=>AB=119m; AC=255cm

Lời giải:

Ký hiệu độ dài của $BC=a, BH=b, CH=c$ $(a,b,c>0$)

Theo bài ra ta có:

\(\left\{\begin{matrix} S_{AHB}=\frac{ab}{2}=54\\ S_{AHC}=\frac{ac}{2}=96\end{matrix}\right.\Rightarrow \left\{\begin{matrix} ab=108\\ ac=192\end{matrix}\right.(1)\)

\(BC=BH+CH=b+c\Rightarrow BC^2=(b+c)^2(2)\)

Mặt khác, theo định lý Pitago cho các tam giác vuông:

\(BC^2=AB^2+AC^2=AH^2+BH^2+AH^2+CH^2=2a^2+b^2+c^2(3)\)

Từ \((2);(3)\Rightarrow (b+c)^2=2a^2+b^2+c^2\Leftrightarrow a^2=bc\)

Từ (1): \(ab.ac=a^2.bc=108.192\)

\(\Leftrightarrow a^2.a^2=108.192\Rightarrow a=12\) (cm)

\(b=\frac{108}{a}=\frac{108}{12}=9; c=\frac{192}{a}=\frac{192}{12}=16\)

Vậy:

\(AB=\sqrt{a^2+b^2}=\sqrt{12^2+9^2}=15\) (cm)

\(AC=\sqrt{a^2+c^2}=\sqrt{12^2+16^2}=20\) (cm)

\(BC=b+c=9+16=25\) (cm)

Hình vẽ:

a: Xét ΔHBA vuông tại H và ΔABC vuông tại A có

góc B chung

=>ΔHBA đồng dạng với ΔABC

b: \(BC=\sqrt{3^2+4^2}=5\left(cm\right)\)

AH=3*4/5=2,4cm

a. Xét ΔHBA và ΔABC có:

       \(\widehat{H}=\widehat{A}\) = 90⁰ (gt)

        \(\widehat{B}\) chung

\(\Rightarrow\)  ΔHBA \(\sim\) ΔABC (g.g)

b. Vì  ΔABC vuông tại A

Theo đ/lí Py - ta - go ta có:

  BC² = AB² + AC²

  BC² = 3² + 4²

\(\Rightarrow\) BC² = 25 cm

\(\Rightarrow\) BC = \(\sqrt{25}=5\) cm

Ta lại có:  ΔHBA \(\sim\) ΔABC

   \(\dfrac{AH}{CA}=\dfrac{BA}{BC}\) 

\(\Leftrightarrow\dfrac{AH}{4}=\dfrac{3}{5}\) 

\(\Rightarrow\) AH = 2,4 cm

Sửa đề là : S_CHA  nhé 

Ta có : \(\frac{S_{ABH}}{S_{CHA}}=\left(\frac{AB}{CH}\right)^2=\frac{4}{9}\)

\(AB=\sqrt{BH\cdot BC}=\sqrt{1.8\cdot5}=3\)

\(AC=\sqrt{5^2-3^2}=4\)

CH=BC-BH=3,2

\(AH=\dfrac{AB\cdot AC}{BC}=2.4\)

27/12/2017 lúc 18:59

Ex1: Điền từ thích hợp vào chỗ trống

 This is Ba. He(1)......... a student.Every morning he(2).........up at 5.30.He(3).............. his teeth and takes a(4)............... then has breakfast at 6.15. He goes to school(5)........six thirty.His house is(6).............his house so he walks.The classes(7)............at 7.15 and finish at 11.15.In the afternoon he plays sports with his friend,Nam. They play badminton but now they(8).................soccer.In the evening he (9)......his homework and goes to(10).........at 9.30

Ex2:Cho dạng đúng của động từ trong ngoặc

1.My sister(have)...........classes from Monday to Friday

2.She(read)................a book in her room now

3.He(get)........................up at 6.00 every day?

4.There(not be)..............a big yard behind his classroom

27/12/2017 lúc 18:59

Ex1: Điền từ thích hợp vào chỗ trống

 This is Ba. He(1)......... a student.Every morning he(2).........up at 5.30.He(3).............. his teeth and takes a(4)............... then has breakfast at 6.15. He goes to school(5)........six thirty.His house is(6).............his house so he walks.The classes(7)............at 7.15 and finish at 11.15.In the afternoon he plays sports with his friend,Nam. They play badminton but now they(8).................soccer.In the evening he (9)......his homework and goes to(10).........at 9.30

Ex2:Cho dạng đúng của động từ trong ngoặc

1.My sister(have)...........classes from Monday to Friday

2.She(read)................a book in her room now

3.He(get)........................up at 6.00 every day?

4.There(not be)..............a big yard behind his classroom

27/12/2017 lúc 18:59

Ex1: Điền từ thích hợp vào chỗ trống

 This is Ba. He(1)......... a student.Every morning he(2).........up at 5.30.He(3).............. his teeth and takes a(4)............... then has breakfast at 6.15. He goes to school(5)........six thirty.His house is(6).............his house so he walks.The classes(7)............at 7.15 and finish at 11.15.In the afternoon he plays sports with his friend,Nam. They play badminton but now they(8).................soccer.In the evening he (9)......his homework and goes to(10).........at 9.30

Ex2:Cho dạng đúng của động từ trong ngoặc

1.My sister(have)...........classes from Monday to Friday

2.She(read)................a book in her room now

3.He(get)........................up at 6.00 every day?

4.There(not be)..............a big yard behind his classroom

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