Question

Area of a circle inscribed in an equilateral triangle is 154 sq cm . find the perimeter of the triangle

Answer 1

The area of the circle =154cm² and area =πr²

154 = 22/7 × r²

154 × 7/22=r²

49=r²

r =7cm

Let the triangle be ABC the equilateral triangle then AD the altitude =height.

The angle bisectors equal to the altitudes and medians whose point of intersection divide the medians in the ratio 2:1

Let center of circle =O then OD =1/3AD

r=h/3

7=h/3

h=3× 7=21cm

Let each side of the triangle be x then the altitude of the equilateral triangle is √3/2 times its side by Pythagoras theorem.

h=√3x/2

x=2h/√3

(2×21)/√3

42/1.7321=24.2480

x=24.2480cm

Perimeter =24.2480 × 3=72.744cm