the area of a circle inscribed in an equliateralal triangle in 616cm2. find the parameter of the triangle.
pl.give full solution
If r is the radius of the inscribed circle i.e. the radius of the incircle of the triangle, then there's a formula, which connects r, the area of the triangle and the perimeter of the triangle.
r=area of the circle/perimeter of the circle.
Let the side of the equilateral triangle be a.
So perimeter =3a
We are given that,
area of the inscribed circle is 616 sq. cm.
solving we get,
Substitute this value in the formula for area of the triangle and the perimeter.
This will give you the value of a.