[tex]A_{totala}=2(ab+bc+ac) \\ \\ Din~ax=by=cz=6~si~din~a,b,c,x,y,z \in N,~deducem~ca \\ \\ a,b,c~sunt~divizori~naturali~ai~lui~6. \\ \\ Deci~a,b,c \in \{1;2;3;6 \}. \\ \\ Si~tinand~cont~ca~a\ \textless \ b\ \textless \ c,~avem~urmatoarele~posibilitati: \\ \\ (a,b,c) \in \{(1,2,3);(1,2,6);(1,3,6);(2,3,6)\} \\ \\ Pentru~(a,b,c)=(2,3,6)~se~obtine~aria~maxima. \\ \\ A_{t.max}=2(2 \cdot 3+3 \cdot 6+2 \cdot 6)= 72~cm^2.[/tex]
