Question

A wire is bent to form a equilateral triangle and it encloses an area of A cm sq. .If the same wire is bent to form a circle ,then the area of circle would be.

Answer 1

let the side of triangle is a
(√3/4)a^2 = A
a = √ 4*A / √3
a = 2 √ A/ √3
3a = 6√A/ √3
perimeter of triangle = circumference of circle
6√A/ √3 = 2 *π* r
r = 3√ A / √3 π
r = √3 *√ A / π
area = π *r*r
area = π * (√3*√ A / π) * (√3* √A/ π)
area = 3A / π = 21 A/22

Answer 2

Answer:

Step-by-step explanation:

let the side of triangle is a

(√3/4)a^2 = A

a = √ 4*A / √3

a = 2 √ A/ √3

3a = 6√A/ √3

perimeter of triangle = circumference of circle

6√A/ √3 = 2 *π* r

r = 3√ A / √3 π

r = √3 *√ A / π

area = π *r*r

area = π * (√3*√ A / π) * (√3* √A/ π)

area = 3A / π = 21 A/22