In a ∆ABC, the bisector of ∠A meets BC at D. IF AB = 9.6 cm, AC = 11.2 cm and BD = 4.8 cm, the perimeter (in cm) of ∆ABC is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 31.2
Concept used:
According to the angle bisector theorem, an 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.
Calculations:
According to the concept,
⇒ AB/AC = BD/DC
⇒ 9.6/11.2 = 4.8/DC
⇒ DC = 5.6
So, BC = 5.6 + 4.8 = 10.4
Perimeter of triangle ABC = 9.6 + 10.4 + 11.2 = 31.2