ABC is a right angle triangle and AB = 5 cm, BC = 12 cm and ∠ABC
| ABC is a right angle triangle and AB = 5 cm, BC = 12 cm and ∠ABC is 90°. If AD is angle bisector, then find the value of AD.
A. 7√2 cm
B. 5/√3 cm
C. 5√13/3 cm
D. 5/√13 cm
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
right triangle ABC
AC2 = AB2 + BC2
AC2 = 52 + 122 = 25 + 144 = 169
AC = √169 = 13 cm
IF AD is bisector of ∠BAC, then
AB/AC = BD/DC
5/13 = BD/DC
DC = 13BD/5
BD + DC = BC
BD + 13BD/5 = 12
18BD/5 = 12
BD = 12 × (5/18) = 10/3
In right triangle ABD
AD2 = AB2 + BD2
AD2 = 52 + (10/3)2 = 25 + 100/9 = 325/9
AD = √325/9 = 5 √13/3 cm
