Explicație pas cu pas:
P = AB + BC + AC = 47 cm
[tex]\frac{AB}{ \frac{1}{3} } = \frac{BC}{ \frac{1}{4} } = \frac{AC}{ \frac{1}{5} } = k \\ [/tex]
[tex]AB = \frac{k}{3}; \: BC = \frac{k}{4}; \: AC = \frac{k}{5} [/tex]
[tex]AB + BC + AC = \frac{k}{3} + \frac{k}{4} + \frac{k}{5} \\ = \frac{20k + 15k + 12k}{60} = \frac{47k}{60} \\ 47 = \frac{47k}{60} = > k = 60[/tex]
[tex]AB = \frac{k}{3} = \frac{60}{3} = 20 = > AB = 20 \: cm \\ [/tex]
[tex]BC = \frac{k}{4} = \frac{60}{4} = 15 = > BC = 15 \: cm \\ [/tex]
[tex]AC = \frac{k}{5} = \frac{60}{5} = 12 = > AC = 12 \: cm \\ [/tex]
