Question

In the adjoining figure, if AD is the bisector of ∠A, what is AC?

Answer 1

||✪✪ QUESTION ✪✪||

In the adjoining figure, if AD is the bisector of ∠A, what is AC ?

|| ★★ FORMULA USED ★★ ||

→ The Angle-Bisector theorem :- if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.

So, From image , we can say That :-

c/b = b/n

|| ✰✰ ANSWER ✰✰ ||

As , Given in Question,

→ AB = c = 6cm.

→ AC = b = Let x cm.

→ BD = m = 3cm.

→ DC = n = 2cm.

So, By Angle-Bisector theorem , Putting values we get :-

→ c/b = m/n

→ 6/x = 3/2

Cross - Multiplying

→ 3x = 12

Dividing both sides by 3,

→ x = 4 cm.

Hence, Side AC length is 4cm.

Answer 2

Answer:

4 cm

Step-by-step explanation:

Given:

In ∆ABC,

AD is the bisector of angle A.

Then,

$\frac{BD}{DC} = \frac{AB}{AC} \\ \\ \frac{3}{2} = \frac{6}{AC}$

After cross multiplication we get,

$3AC = 12 \\ \\ AC = \frac{12}{3} \\ \\ AC = 4 \: cm$