Question

in triangle abc angle C equals to 90 degree AC is equal to 5cm BC is equal to 12 centimetre the bisector of angle a meets BC at D what is the length of AD​

Answer 1

In a triangle ABC , angle C=90° ,AC=5cm , BC=12cm. The bisector of angle a meets BC at D. The length of AD = 4.61cm^2.

Stepwise explanation is given below:

- It is given that the AC=5cm, BC=12cm.

area of triangle = (1/2) × base×height

- If we take AC as perpendicular then BC will be base.

- Then area of triangle = (1/2)× 5×12 = 30 cm²

also, by Pythagoras' theorem, 

BC² = AC² +BC²

       =(5)² + (12(² = 169

⇒BC = 13 cm

now, if AD is perpendicular then AB is the base

- Area of triangle = (1/2)× AB ×AD

⇒30 = (1/2)× 13×AD

⇒AD = 60/13 =4.61 cm

Answer 2

The length of AD = 5√2 cm

Step-by-step explanation:

Triangle ABC with right angle from C is given in figure.

We know that angle bisector is a line that divides an angle into two half.

Here AC = 5 cm

BC = 12 cm                                         (given)

$\textbf{\Large Using Pythagorus Theorem :} a^2 + b^2 = c^2$

So

$5^2 + 12^2 = AB^2 \\\\25 + 144 = 169 = AB^2$

So AB = 13 cm

Now It is given that a bisector from A meets at D on the libe BC,

which makes angle DAC = 45°

So

By trigonometry

Cos 45° = $\frac{\textbf{\large AC}}{\textbf{\large AD}} = \frac{ 1}{\sqrt 2}$

As We know that AC = 5cm

$\textbf{\large So the length of side AD}= 5\sqrt 2$   cm             (Answer)