Question

the area of incircle of an equilateral triangle is 154cm^2, what is the perimeter of the triangle

Answer 1

Answer:

72.7 cm

Step-by-step explanation:

Let r be the radius of the circle.

πr² = 154

⇒ (22/7) * r² = 154

⇒ r² = 49

⇒ r = 7 cm.

Let a be the sides of triangle and its height be h.

Then, r = (1/3)h

h = 3r

h = 3 * 7

h = 21 cm.

Then,

h = √3/2a

⇒ a = (2/√3) * h

      = (2/√3) * 21

     = (42/√3)

     = 14√3 cm

Perimeter of the triangle = 3a

= 3(14√3)

= 42√3

= 42 * 1.732

= 72.7 cm

Hope it helps you

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