In triangle ABC, 'D' is a point on BC such that ∠BAD = ∠DAC. If AB = 24, AC = 16 and BC = 12.5, then find the length of BD.
Show answer & explanation
Correct answer: B
Explanation
Given:
AB = 24
AC = 16
BC = 12.5
∠BAD = ∠DAC
By the formula:
Angle Bisector Theorem
BD / DC = AB / AC
BD / DC = 24 / 16 = 3 / 2
Let
BD = 3x, DC = 2x
BC = BD + DC
12.5 = 3x + 2x
12.5 = 5x
x = 2.5
BD = 3x = 3 × 2.5 = 7.5 cm