Question

cerințe: Masurile arcelor AB AC si BC

Answer 1

Răspuns:

p.s.  aplicate proportii derivate...

Explicație pas cu pas:

Prin AC, AB, BC vom înțelege arce ...

(AC, AB, BC) i.p. (0,(3), 0,1(6), 0,(1)), ⇒

$\dfrac{AC}{0,(3)}= \dfrac{AB}{0,1(6)}=\dfrac{AB}{0,(1)}, ~~deoarece~0,(3)=\frac{3}{9}=\frac{1}{3},~~0,1(6)=\frac{16-1}{90}=\frac{15}{90}=\frac{1}{6},~~0,(1)=\frac{1}{9},~obtinem \\\dfrac{AC}{\frac{1}{3}}=\dfrac{AB}{\frac{1}{6}}=\dfrac{BC}{\frac{1}{9}}=\dfrac{AC+AB+BC}{\frac{1}{3}+\frac{1}{6}+\frac{1}{9}}=\dfrac{360}{\frac{6+3+2}{18} }=\dfrac{360*18}{11} \\Deci,~~AC=\dfrac{1}{3}*\dfrac{360*18}{11}=\dfrac{360*6}{11}=\dfrac{2160}{11}$

$AB=\dfrac{1}{6}*\dfrac{360*18}{11}=\dfrac{360*3}{11}=\dfrac{1080}{11}\\BC=\dfrac{1}{9}*\dfrac{360*18}{11}=\dfrac{360*2}{11}=\dfrac{720}{11}$