Question 11

In a triangle ABC, AD is the bisector of angle A. If AC =4.2 cm, DC = 6 cm, BC =10 cm, find AB.

Solution

In a triangle, the angular bisector divides the side which it intersects in the ratio of other two sides.

So, In the triangle ABC, the angular bisector AD divides the side BC in the ration of AB and AC

$$\Rightarrow$$ BD : DC = AB : AC

Given BC = 10 cm and DC = 6 cm

$$\Rightarrow$$ BD = BC - DC = 10 - 6 = 4 cm

Then $$AB =\frac{BD}{DC}\times AC = \frac{4}{6}\times 4.2 = 2\times 1.4 = 2.8$$ cm

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