Question

2 pls repede ca imd am mate

Answer 1

Răspuns:

Explicație pas cu pas:

K= CONSTANTA

6a=4b=3c=K

a= k/6

b=k/4

c=k/3

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a+b+c =180 ( suma unghiurilor unui triunghi )

²⁾k/6+³⁾k/4+⁴⁾k/3=¹²⁾180 (am adus la acelasi (12)numitor amplificand fractiile )

2k+3k+4k=2160

9k=2160

k=2160:9

k= 240

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înlocuim K cu ..240

avem

a= k/6=240/6= 40

b= k/4=240/4= 60

c= k/3= 240/3=80

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deci unghiurile sunt

a=40

b=60

c=80

Answer 2

$\it Fie\ x,\ y,\ z\ m\breve asurile\ celor\ trei\ unghiuri.\\ \\ x+y+z=180^o\ \ \ \ \ (1)\\ \\ \{x,\ y,\ z\}\ i.\ p.\ \{6,\ 4,\ 3\} \Rightarrow 6x=4y=3z=k \Rightarrow \begin{cases}\it x=\dfrac{k}{6}\\ \\ \it y=\dfrac{k}{4}\\ \\ \it x=\dfrac{k}{3}\end{cases}\ \ \ \ (2)$

$\it \dfrac{k}{6}+\dfrac{k}{4}+\dfrac{k}{3}=180^o|_{\cdot12} \Rightarrow 2k+3k+4k=12\cdot180^o \Rightarrow 9k=12\cdot180^o|_{:9}\Rightarrow\\ \\ \\ \Rightarrow k=12\cdot20^o \Rightarrow k=240^o\ \ \ \ \ (3)\\ \\ \\ (2),\ (3) \Rightarrow \begin{cases} \it x=\dfrac{240^o}{6}=40^o\\ \\ \it y=\dfrac{240^o}{4}=60^o\\ \\ \it z=\dfrac{240^o}{3}=80^o\end{cases}$