In triangle ABC, the bisector of angle A meets side BC at point D. If AB = 28 cm, AC = 42 cm, and BC = 50 cm, find the length of BD.
Show answer & explanation
Correct answer: C
Explanation
Given:
AB = 28 cm
AC = 42 cm
BC = 50 cm
Angle Bisector Theorem:
BD / DC = AB / AC
BD / DC = 28 / 42 = 2 / 3
Let:
BD = 2x, DC = 3x
BC = BD + DC
50 = 2x + 3x
50 = 5x
x = 10
BD = 2x = 20 cm