The perimeter of △ABC is 49 cm. The angle bisector of ∠A meets BC at M. BM = 6 cm, MC = 8 cm. Find AC.
Given perimeter = 49 cm
BC = BM + MC = 6 + 8 = 14 cm
AB + AC = 49 - 14 = 35 cm
Since AM is the angle bisector of ∠A,
ABAC=BMMC
ABAC=68=34
Adding 1 on both sides, we have
ABAC+1= 34+1
⇒AB+ACAC = 74
⇒35AC = 74
⇒AC = 35×47
= 20 cm