In ∆ABC, AD is the bisector of ∠A meeting BC at D. If AC = 21cm, BC = 11cm and the length of BD is 3 cm less than DC, then the length (in cm) of side AB is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 12.
Let BD = x so DC becomes x + 3.
BC = 11cm
2x + 3 = 11
x = 4.
By using the angle bisector theorem one gets,
AB/BD = AC/DC
AB = (AC × BD)/DC
AB = (21 × 4)/7 = 12 cm.