Question

the area of a circle inscribed in a in a equilateral triangle is 154 cm square find the perimeter of the triangle take root 3 equals to 1.7 to 3​

Answer 1

Area of the circle = 154 sq cm

therefore, πr²=154 cm²

or,22r²/7=154 cm²

or,r²=154 cm²*7/22=49 cm²

or,r=7 cm.

Let the side of the triangle be x cm.

Therefore, semi perimeter=3x/2

Radius of the circle=Area/Semi Perimeter of Δ.

or,7=(√3/4*x²)/(3x/2)

or,7=(√3*x)(3*2)

or,7=(√3*x)/6

or,7*6=√3*x

or,42=√3*x

or,42/√3=x

or,x=42/√3

Perimeter=42/√3*3=42√3=42*1.73=72.66 cm.