Question

in triangle ABC,length of sides a=12,b=13,c=5,then find the length of angular bisectors​

Answer 1

The length of bisector,  AD = 12.2 cm

Step-by-step explanation:

Given,

In triangle ABC,

a  = 12, b = 13 and c = 5

Let A be internal bisector of angle A.

By Angle Bisector Theorem ,

$\dfrac{12}{13}=\dfrac{x}{5-x}$

By cross-multiplying, we get

13(x) = 12(5 - x)

⇒ 13x= 60 - 12x

⇒ 13x + 12x = 60

⇒ 25x = 60

⇒ x = $\dfrac{60}{25} =\dfrac{12}{5}=2.4$

In triangle ABD,

∠B = 90°

∴ The length of bisector,

AD $=\sqrt{12^2+2.4^2}$

$=\sqrt{144+5.76}$

$=\sqrt{149.76}$

= 12.2 cm

Similarly, we can find the remaining lengths of bisectors.

∴ The length of bisector,  AD = 12.2 cm