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Question
The area of incircle of an equilateral triangle is 154 cm2 . The perimeter of the triangle is
Options
71.5 cm
71.7 cm
72.3 cm
72.7 cm
Solution
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`
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