Question

In a ΔABC, AB = 5 cm, AC = 10 cm and BC = 9 cm, then the length of angle bisector AD is

Answer 1

Answer:

I think the answer is '5'

I hope it will help you

Answer 2

$\sf\huge\bold{Answer:}$

Given :

• ΔABC
• AB = 5 cm
• AC = 10 cm
• BC = 9 cm

To find :

• Length of line bisector of AD

Solution :

In given figure, it can be seen that AD bisects BC into two equal lengths

CD = BD = ½BC = 4.5cm

Now, the bisector drawn from A to BC is perpendicular to BC [assumption]

∠ADB=∠ADC=90°

So, ∆ADB and ∆ADC for right angled triangles

In ∆ ADB

• Using Pythagoras theorem

→H²=B²+P²

→ AB²=BD²+AD²

→5²=(4.5)²+AD²

→25=20.25+AD²

→25-20.25=AD²

→AD²=4.75

→AD=√4.75

→AD≈2.179

→AD≈2.2

In ∆ADC

• Using Pythagoras theorem

→H²=B²+P²

→ AC²=CD²+AD²

→10²=(4.5)²+AD²

→100=20.25+AD²

→100-20.25=AD²

→AD²=79.75

→AD=√79.75

→AD≈8.93

→AD ≈ 8.9