Question

In triangleABC AD is the bisector of angle A .If AB=10cm,AC=14cm,BC=6cm find BD and DC

Answer 1

Answer:

Step-by-step explanation:

According to angle bisector theorem,

DB/DC=AB/AC

x/(6-x)=10/14

14x=10(6-x)

14x=60-10x

14x+10x=60

24x=60

x=60/24

x=5/2

BD=x

    =2.5

DC=6-x=6-2.5

     =3.5cm

Answer 2

Answer:

The length of BD is 2.5 cm and length of DC is 3.5 cm.

Step-by-step explanation:

Given information: In triangle ABC, AD is the bisector of angle A, AB=10cm,AC=14cm,BC=6cm.

According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Let BD=x, so DC=6-x.

Using angle bisector theorem, we get

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

$\frac{10}{14}=\frac{x}{6-x}$

$\frac{5}{7}=\frac{x}{6-x}$

On cross multiplication we get

$5(6-x)=7x$

$30-5x=7x$

$30=7x+5x$

$30=12x$

Divide both sides by 12.

$\frac{30}{12}=x$

$2.5=x$

$DC=6-x=6-2.5=3.5$

Therefore, the length of BD is 2.5 cm and length of DC is 3.5 cm.