Question

in trianlge ABC , AD is the bisector of angle BAC . if AB = 6cm , AC = 5cm and BD = 3cm , then DC=?

de options r...

a. 11.3cm

b. 2.5cm

c. 3.5cm

d. none.

why?plzz answer!!!

Answer 1

answer is b I.e 2.5cm

Answer 2

So, Answer is $b$

Step-by-step explanation:

Given,

$\triangle ABC$ , $AD$ is the bisector of $\angle BAC$, $AB=6cm$ , $AC=5cm$ and $BD=3cm$

From figure,

$\triangle ABD$ and $\triangle ACD$

• $\angle BAD=\angle CAD$ given
• $\angle ADB=\angle ADC$
• $AD$ is common.

∴ $\triangle ABD$≅$\triangle ACD$

∴ $\frac{AB}{BD}=\frac{AC}{CD}$

Plug all the value in above equation,

⇒$DC=\frac{BD}{AB}\times AC$

⇒$DC=\frac{3}{6}\times 5$

∴ $DC=2.5$

∴ The length of $DC$ is $2.5cm$