Question

In a ΔABC , AD is the bisector of ∠A , 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.

Answer 1

Triangle

Step-by-step explanation:

Given: In a ΔABC , AD is the bisector of ∠A , meeting side BC at D.

So we know that AB/AC = BD/DC

(i) BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm.

  DC = AC * BD / AB = 2.5 * 4.2 /5 = 2.1cm    

(ii) BD = 2 cm, AB = 5 cm and DC = 3 cm.

  AC = AB * DC / BD = 5 * 3 / 2 = 15/2 = 7.5cm

(iii) AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm.

 BD = AB * DC / AC = 3.5 * 2.8 / 4.2 = 2.33cm

(iv) AB = 10 cm, AC = 14 cm and BC = 6 cm

 BD/DC = AB/AC = 10/14 = 5/7

 BD = 5/12 * 6 = 2.5cm

 DC = 7/12 * 6 = 3.5cm

 

(v) AC = 4.2 cm, DC = 6 cm and BC = 10 cm

   AB/4.2 = 4/6 (as BD = BC- DC)

   AB = 2/3 *4.2 = 2.8cm

(vi) AB = 5.6 cm, AC = 6 cm and DC = 6 cm.

     BD = DC * AB/AC = 6 * 5.6/ 6 = 5.6cm

     BC = BD + DC = 5.6cm + 6 cm = 11.6cm

(vii) AB = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.

    DC = BC - BD = 6 - 3.2 = 2.8cm

     AC = AB * DC/BD = 5.6 * 2.8 / 3.2 = 4.9cm

(viii) AB = 10 cm, AC = 6 cm and BC = 12 cm

    BD/DC = AB/AC = 10/6 = 5/3

   BD = 5/8 * 12 = 7.5cm

   DC = BC - BD = 12 - 7.5 = 4.5cm

Answer 2

AD is the bisector of ∠A , meeting side BC at D. =>  AB /AC  = BD/CD

Step-by-step explanation:

In a ΔABC , AD is the bisector of ∠A , meeting side BC at D

=>  AB /AC  = BD/CD

(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.

=>  5/4.2  = 2.5/DC

=> DC = 2.1 cm

(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.

=> 5/AC = 2/3

=> AC = 7.5 cm

(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

=> 3.5/4.2   = BD/2.8

=> BD = 7/3 cm

Find all other same way

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