[tex]a;b \ \ \ d.p. \\ 6;3 \\\\ \longrightarrow \frac{a}{6}=\frac{b}{3}=k \\\\ a=6k \\ b=3k \\\\\\ a)0,(3) \to \frac{3}{9}=\frac{1}{3} \\\\ 0,1(6)=\frac{16-1}{90}=\frac{15}{90}=\frac{1}{6} \\\\\\ b;c \ \ \ i.p. \\\\ \frac{1}{3}; \frac{1}{6} \\\\\\ \longrightarrow b*\frac{1}{3}=c*\frac{1}{6}=k \\\\ b=3k \\ c=6k \\\\\\ b) a^2+b^2+c^2=225 \\\\ (6k)^2+(3k)^2+(6k)^2=225 \\\\ 36k^2+9k^2+36k^2=225 \\\\ 81k^2=225 \\\\ k^2=\frac{225}{81} \\\\ k=\sqrt{\frac{225}{81}} \\\\ \underline{k=\frac{15}{9}}[/tex]
[tex]a=6*\frac{15}{9}} \\\\a=2*\frac{15}{3} =2*5=10 \\\\ \boxed{a=10} \\\\ b=3* \frac{15}{9}=\frac{15}{3}=5 \\\\ \boxed{b=5} \\\\ c=6*\frac{15}{9}= 2*5=10 \\\\ \boxed{c=10}[/tex]
