Question

do it fast with explaination

Answer 1

Area of equilateral triangle is √3

⇒ √3 a²/4 = √3

⇒ a² = 4

⇒ a = 2

 For any Equilateral Triangle

The radius of Incircle = (Side/ 2√3)
                                  = 2/2√3 = 1/√3
Circumference = 2$\pi$r
                         = 2$\pi$1/√3
                         = 2/√3 × $\pi$

Answer 2

area of an equilateral ∆ = √3 m²
√3/4 × (side length) ² = √3

side length = 2 m

now,

, radius of circle divide the triangle into 3 parts .

area of sum of three pàrts = area of ∆
1/2 × r × L + 1/2 × r × L + 1/2 × r × L = √3

3/2 × ( r ) × L = √3

3/2 × r × 2 = √3

r = 1/√3

so, radius of circle = 1/√3 m

circumstance = 2πr = 2π/√3 m