Question

The area of incircle of an equilateral triangle is 154 cm² . The perimeter of the triangle is

पर्याय

• 71.5 cm

• 71.7 cm

•  72.3 cm

• 72.7 cm

Answer 1

Area of incircle of equilateral triangle is `154 cm^2`

We have to find the perimeter of the triangle. So we will use area to get,

Area of incircle=`154`

`pir^2=154`

`r =sqrt(154/pi) cm`

As triangle is equilateral so,

`∠ OCM=30°`

So, 

`tan 30°=r/MC`

`MC=sqrt((154(3))/pi) cm`

So, 

`AC=2(MC)`

`=2((sqrt154(3))/pi)cm`

Therefore perimeter of the triangle is, 

`= 3(AC)`

`= 6(sqrt462/3.14)`

`=72.7 cm`