Question

In the given figure, AD bisects $\angle$. If $AB=18$ cm, $AC=24$ cm and $BC=28$ cm then length of CD is

• A. $12$ cm
• B. $8$ cm
• C. $20$ cm
• D. $16$ cm

Answer 1

The correct option is D $16$ cm

As given,

$AB=18cm,AC=24cm,BC=28cm$

and $AD$ is bisector of angle $A$

$\therefore \frac{BD}{DC}=\frac{AB}{AC}=\frac{18}{24}=\frac{3}{4}$

$⟹BD=\frac{3}{4}CD$

$BC=28$

$⟹BD+DC=28⟹\frac{3}{4}CD+CD=28$

$⟹\frac{7}{4}CD=28$

$⟹CD=16cm$