Răspuns:
3,75cm; 10cm; 11,25cm.
Explicație pas cu pas:
Fie AM este bisectoare in ΔABC, M∈BC, BM=2,5cm, CM=7,5cm.
Atunci BC=BM+CM=10cm. Perimetrul(ΔABC)=25cm.
[tex]Dupa~Teorema~Bisectoarei~\frac{BM}{AB}=\frac{CM}{AC},~\frac{2,5}{AB}=\frac{7,5}{AC},~deci~\frac{AC}{AB}=\frac{7,5}{2,5}=3,~deci~AC=3AB.\\[/tex]
AB+BC+AC=25cm, ⇒AB+10+3·AB=25, ⇒4·AB=15, ⇒AB=15:4=3,75cm
Atunci AC=3·3,75=11,25cm
