In triunghiul ABC ~ Tr. MNP => AB/MN=AC/MP=BC/NP = k.
<=> AB = k * MN;
<=> AC = k * MP;
<=> BC = k * NP;
=> AB + BC + AC = k * (MN + MP + NP) <=> 96 = k * 48 => k = 2.
AB = 2 * MN = 2 * 12 = 24 cm.
AC = 2 * MP = 2 * 20 = 40 cm.
BC = 2 * NP = 2 * 16 = 32 cm.