Răspuns:
[tex]\purple{\bf AB = 24}[/tex]
[tex]\pink{\bf AC = 18}[/tex]
[tex]\red{\bf BC = 12}[/tex]
Explicație pas cu pas:
Buna !
[tex]\bf AB+BC+AC=54[/tex]
[tex]\bf \dfrac{AB}{8}= \dfrac{AC}{6} \implies 6\cdot AB = 8\cdot AC \implies AB = \dfrac{8AC}{6}\implies \boxed{\bf AB = \dfrac{4AC}{3}}[/tex]
[tex]\bf \dfrac{BC}{2}= \dfrac{AC}{3} \implies 3\cdot BC = 2\cdot AC \implies \boxed{\bf BC = \dfrac{2AC}{3}}[/tex]
[tex]\bf \dfrac{4AC}{3}+AC+\dfrac{2AC}{3}=54~~~\bigg|\cdot3[/tex]
[tex]\bf 4AC+3AC+2AC=162[/tex]
[tex]\bf 9AC=162~~~\bigg|:9[/tex]
[tex]\pink{\boxed{\bf AC = 18}}[/tex]
[tex]\bf AB = \dfrac{4\cdot\not18}{\not3} \implies AB = 4\cdot 6\implies \purple{\boxed{\bf AB = 24}}[/tex]
[tex]\bf BC= \dfrac{2\cdot\not18}{\not3} \implies BC = 2\cdot 6\implies \red{\boxed{\bf BC = 12}}[/tex]
[tex]\bf Verificare:[/tex]
[tex]\bf 18+ 12 +24 = 54~(adevarat)[/tex]
P.S.: Dacă ești pe telefon te rog să glisezi spre stânga pentru a vedea întreaga rezolvare.
Bafta multa !
