Question

If the area of circle inscribed in an equilateral triangle is 44 square units ,then the perimeter of the triangle( in units) is​

Answer 1

GIVEN:-

Area of a circle = 44unit²

To find :-

Perimeter of the equilateral triangle

Solution:-

Area of a circle = πr²

=>44 = πr²

=>44 = 22/7*r²

=>r² = 44*7/22

=>r² = 14

=>r = √14unit

we know that Centroid of equilateral or any triangle divides each median in ratio 2:1 .

•°• if height of equilateral triangle is AD and O is the centroid,

then, height = 3 *radius of inscribed circle

=>3 * √14

h=3√14

Height of equilateral triangle = √3a/2

{ where , a is the side of equilateral triangle}

3√14= √3 a/2

or,

a=6√14/√3

a=2√3√14

or,

a=2√42

So,

perimeter =3*2√42 = 6√42unit