Răspuns:
Explicație pas cu pas:
a)Aplicam T Thales
AM/MB=AN/NC 3/6=6/NB=1/2 NB =12 cm
AB=AM+MB=3+6=9 cm
AC=6+12=18 cm
aplicam T fundamentala a asemanarii
AM/AB=AN/AC=MN/BC=3/9=1/3 MN=5 5/BC=1/3 BC=15 cm
P=AB+AC+BC=9+18+15=42 cm
b) Aabc=√p(p-a)(p-b)(p-c) formula lui Heron
p=(a+b+c)/2=42/2=21
Aabc=√21(21-9)(21-18)(21-15)=√3·6·4·3·3·6=2·3·6√3=36√3 cm²
