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Question

The perimeter of ABC is 49 cm. The angle bisector of A meets BC at M. BM = 6 cm, MC = 8 cm. Find AC.


A
10 cm
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B
20 cm
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C
15 cm
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D
12 cm
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Solution

The correct option is B 20 cm

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


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