L / 3 = l / 4 = h / 5 = k , unde k > 0; => L = 3k; l = 4k; h = 5k;
insa, 2 ( L * l + L * h + l * h ) = 96 => 12k^2 + 15k^2 + 20k^2 = 48 => 47k^2 = 48 =>
k = 4[tex] \sqrt{3} / \sqrt{47} ;
[/tex]
Apoi, afli imediat L, l si h ;
Pe diagonala AC o calculezi cu formula [tex] \sqrt{ L^{2}+ l^{2}+ h^{2} } ;[/tex]
De asemenea, AB' = [tex] \sqrt{ L^{2}+ h^{2} } ;[/tex]
Iar BC' = [tex] \sqrt{ l^{2}+ h^{2} } ;[/tex]
Bafta!
