Question

If the inradius of an equilateral triangle is 8 cm, then the side of the equilateral triangle is

Answer 1

Answer:

8√3 cm

Step-by-step explanation:

If the inradius of an equilateral triangle is 8 cm, then the side of the equilateral triangle is

Let say Side of equilateral triangle  = X cm

Radius of incircle = 8 cm

Let say Center point of incircle = O  and vertex of trinagles A , B , & C

ΔOAB = ΔOBC = ΔOCA

as OA = OB = OC = Radius = 8 cm

AB = BC = CA = X cm

∠AOB = ∠BOC = ∠COA

∠AOB + ∠BOC + ∠COA = 360°

=> 3∠AOB = 360°

=> ∠AOB = 120°

on ΔOAB

AB² = OA² + OB² - 2OA.OB.Cos120

=> AB² = 8² + 8² - 2* 8 * 8 * (-1/2)

=> AB² = 3 * 8²

=> AB = 8√3

the side of the equilateral triangle  = 8√3 cm