Question

In the figure , AD is the bisector of angle BAC. If AB = 15 cm and AC = 20 cm , find

a) BD : DC

b) Write the ratio of areas of triangle ABD and triangle ADC

c) If area of triangle ABD is 21 cm2 , then find area of triangle ADC​

Answer 1

Step-by-step explanation:

Since AD is the bisector of ∠A.

∴

AC

AB

=

DC

BC

⇒

14

10

=

6−x

x

⇒

7

5

=

6−x

x

⇒ 30−5x=7x

⇒ 12x=30

⇒ x=

2

5

=2.5cm

⇒ BD=2.5cm and

DC=(6−x)cm=(6−2.5)cm=3.5cm