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The area of a circle inscribed in an ...

The area of a circle inscribed in an equilateral triangle is `154\ c m^2` . Find the perimeter of the triangle. `[U s e\ \ pi=22//7a n d\ sqrt(3)=1. 73]`

Text Solution

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The correct Answer is:
`72.66cm`
Let the radius of the circle be `rcm`
The, `pir^(2)=154impliesr^(2)=(154xx7/22)impliesr=7cm`
Let each side of the triangle be `acm` and its heigh t be `h` cm.
Then `r=h/3impliesh=3r=21cm`

`h=sqrt(a^(2)-(a^(2))/4)=(sqrt(3)a)/2implies(sqrt(3)a)/2=21`
`:.a=42/(sqrt(3))xx(sqrt(3))/(sqrt(3))=14sqrt(3)`
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