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