Question

In $\triangle ABC$, the bisector of ∠A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

Answer 1

Answer:

The value of BD is 12 cm.

Step-by-step explanation:

Given :  

In ∆ ABC,the bisector ∠A intersects BC in D. AB = 18 cm, AC = 15 cm and AC = 22 cm

In ΔABC, AD is the bisector of ∠A

AB/AC = BD/DC

[The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle]

AB/AC = BD/(BC - BD)

18/15 = BD/ (22 - BD)

6/5 = BD/ (22 - BD)

5BD = 6(22 - BD)

5BD = 132 - 6BD

5BD + 6BD = 132

11BD = 132  

BD = 132/11

BD = 12 cm  

Hence, the value of BD is 12 cm.

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Answer 2

$\huge\red{Solution}$

In $\triangle ABC$,

The bisectors of ∠A intersects BC in D .

And ....

• AB = 18 cm

• AC = 15 cm

• BC = 22 cm

• BD = ??

Solve :

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

$\frac{AB}{AC}= \frac{BD}{DC}$

[The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle]

$\frac{AB}{AC}= \frac{BD}{(BC - BD )}$

=> $\frac{18}{15}= \frac{BD}{(22- BD )}$

=> $\frac{6}{5}= \frac{BD}{(22- BD )}$

=> 5BD = 6 (22 - BD )

=> 5BD = 132 - 6BD

=> 5BD + 6BD = 132

=> 11BD = 132

=> $BD = \frac{132}{11}$

=> BD = 12 cm

Hence , BD = 12cm .