Question

The circle is inscribed in an equilateral if the area of the circle is 462 cm square then the perimeter of the triangle is

Answer 1

Answer:

Perimeter of triangle is 252 cm.

Step-by-step explanation:

➡️ Radius of in-circle (circle inscribed in triangle) =

area / semi perimeter

Area of circle = 462 cm^2

462 cm^2 = pi ☓ r^2

462 = 22/7 ☓ r^2

21 ☓ 7 = r^2

147 = r^2

✔️ 7 root 3 = r.

Now,

➡️r = root3 a^2 /4 /3a

7 root 3 = root 3 a/ 4 ☓ 1/3

7 = a/4 ☓ 1/3

7 = a/12

a = 12 ☓ 7

a = 84 cm

Side of equilateral triangle is 84 cm.

Perimeter of equilateral triangle = 3 ☓ side.

Perimeter of triangle = 3 ☓ 84 cm

Perimeter = 252 cm.