In a 
, AD is the bisector of 
, meeting side BC at D.
(i) If BD = 2.5 cm, AB = 5 cm and AV = 4.2 cm, find DC.
(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AB = 5.6 cm, AC = 6 cm and DC = 6 cm, find BC.
(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.
(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.
(i) we have
Angle BAD=CAD
Here AD bisects ∠A
BD/DC=AB/AC
2.5/DC=5/4.2
DC=2.5*4.2/5
DC=2.1 cm
(ii) Here AD bisects ∠A
AB/DC=AB/AC
2/3=5/AC
AC=15/2
AC=7.5 cm
(iii) in △ ABC A bisects ∠A
BD/DC=AB/BC
BD/2.8=3.5/4.2
BD=3.5*2.8/4.2
BD=7/3
BD=2.33 cm
(iv) In△ABC, AD bisects ∠A
BD/DC=AB/AC
X/6-x =10/14
14x=60-10x
14x+10x=60
24x=60
x= 60/24
x=5/2
x=2.5
BD=2.5
DC= 6-2.5
DC=3.5
(v) AB/AC=BD/DC
AB/4.2=BC-DC/DC
AB/4.2=10-6/6
AB/4.2=4/6
AB=4*4.2/6
AB=2.8 cm
(vi) BD/DC=AB/AC
BD/6=5.6/6
BD=5.6
BC= BD+DC
BC=5.6+6
BC=11.6 cm
(viii) In△ABC, AD bisects ∠A
AB/AC=BD/DC
5.6/AC=3.2/BC-BD
5.6/AC=3.2/6-3.2
5.6/AC=3.2/2.8
AC*3.2=2.8*5.6
AC=2.8*5.6/3.2
AC=7*0.7
AC=4.9 cm
(ix) let BD=x,then DC=12-X
BD/DC=AB/BC
x/12-x= 10/6
6x=120-10x
6x+10x=120
16x=120
x=120/16
x= 7.5
BD=7.5 cm
DC =12-x
DC=12-7.5
DC=4.5 cm