The bisector of ∠B in ΔABC meets AC at D. If AB = 12 cm, BC = 18 cm and AC = 15 cm, then the length of AD(in cm) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6.
Given: AB = 12 cm, AC = 15 cm, BC = 18 cm
We know, The angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
i.e. AB/BC = AD/CD
⇒ 12/18 = AD/CD ⇒ AD/CD = 2/3
⇒ CD = (3/2) × AD
We have, AD + CD = 15
⇒AD + (3/2) × AD = 15
⇒ AD × (5/2) = 15
⇒ AD = 6 cm