Question

In triangle ABC, AD is the bisector of angle A. If BC = 10 cm, BD = 6cm and AC = 6 cm, find AB.

Answer 1

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Answer 2

Answer:

9 cm

Step-by-step explanation:

Given information: In triangle ABC, AD is the bisector of angle A, BC = 10 cm, BD = 6 cm and AC = 6 cm.

We need to find the measure of AB.

$BD+CD=BC$

$6+CD=10$

Subtract 6 from both sides.

$CD=10-6$

$CD=4$

Using angle bisector theorem:

$\frac{AB}{6}=\frac{6}{4}$

On cross multiplication we get

$4\times AB=6\times 6$

$4AB=36$

Divide both sides by 4.

$AB=\frac{36}{4}$

$AB=9$

Therefore the measure of AB is 9 cm.