In triangle ABC, AD is the angle bisector of angle A. If AB = 8.4 cm and AC = 5.6 cm and DC = 2.8 cm, then the length of side BC will be:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 7 cm.
The angle bisector of a triangle bisects the opposite side in such a way that the ratio of the two line segments is proportional to the ratio of the other two sides.
BC = BD + DC
In triangle ABC,
⇒ AB/BD = AC/DC
⇒ 8.4/BD = 5.6/2.8
⇒ BD = 4.2
Hence, BC = 4.2 + 2.8 = 7 cm