Question : In triangle ABC, AD is the angle bisector of angle A. If AB = 8.4 cm, AC = 5.6 cm and DC = 2.8 cm, then the length of side BC will be:
Option 1: 4.2 cm
Option 2: 5.6 cm
Option 3: 7 cm
Option 4: 2.8 cm
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Correct Answer: 7 cm
Solution : The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle. So, $\frac{AB}{AC} = \frac{BD}{DC}$ ⇒ $\frac{8.4}{5.6} = \frac{BD}{2.8}$ ⇒ $\frac{8.4}{2} = BD$ ⇒ $4.2\mathrm{\ cm} = BD$ And, $BD + DC = BC$ ⇒ $BC = 4.2 + 2.8$ ⇒ $BC = 7\mathrm{\ cm}$ Hence, the correct answer is 7 cm.
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