Question

triangle ABC is an equilateral triangle and AD is an angle bisector of angle A , AD=3cm
1. find AC?
2.find the perimeter of triangle ABC?​

Answer 1

Answer:

Step-by-step explanation:

As the triangle ABC is an equilateral triangle

Hence ,

AB= BC = AC .......(1)

ANGLE ABC = ANGLE BAC = ANGLE BCA=60 ......property......(2)

Now AD Is the angle bisector

Hence , angle BAD = angle CAD = 30

AD IS ALSO PERPENDICULAR TO BC .......property

Now in triangle ADC

Angle ADC = 90

AD = 3

Angle DAC = 30

Hence sin 30 = AD / AC

1/2 = 3/AC

HENCE

AC= 3×2

AC = 6

PERIMETER = 6+6+6

= 18

HENCE SOLVED

I HOPE YOU GET IT !!

Answer 2

In an equilateral triangle, height =root3/2*side,,
=>root3/2*side=3=>side=2/root3*3=2root3. AC=2root3. And perimeter =2root3*3=6root3•