Question

AD is the angle bisector of A in triangle ABC. AB:AC=3:4 area of triangle ABD =27 cm². find area of triangle ADC ​

Answer 1

In ∆ABC AD is bisector of angleA

Here AB=3 AC=6 and BC=3√3

Now AB/AC=3/6=1/2

According to angle bisector law BD/DC should be 1/2

Since BC=3√3 therefore BD=√3 and DC=2√3

Then we have BD/DC=√3/2√3=1/2

Again here AB^2 +BC^2=AC^2

Therefor it is a right angle traingle and angle B=90°

Hence from right angle ∆ABD we have

AD^2=AB^2+BD^2

Or, AD^2=(3)^2+(√3)^2

Or, AD^2=9+3

Or, AD^2=12

Or, AD=√12

Or, AD=2√3