Multiple choice

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 :

  1. 4.2 cm

  2. 5.6 cm

  3. 7 cm

  4. 2.8 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the Angle Bisector Theorem, AD divides BC proportionally to the adjacent sides: BD/DC = AB/AC. Given AB = 8.4 cm, AC = 5.6 cm, and DC = 2.8 cm, we get BD/2.8 = 8.4/5.6 = 3/2. Therefore BD = 2.8 × (3/2) = 4.2 cm. The full length BC = BD + DC = 4.2 + 2.8 = 7 cm.

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