Question

the perimeters of a circular and square fields are equal it the area of the square field is 484 m square then the diameters of the circular field is

Answer 1

Answer:

R= 14cm

Step-by-step explanation:

*The perimeter of a circular and square field are equal.

The area of square = 484 sq. cm

*The side of a square will be = 22cm

Perimeter of a square = 4 × 22cm = 88cm

The perimeter of circular field = 88cm

The perimeter of a circle = 2πr

*2πr = 88cm

R = 88cm / (2π)

R= 88/2 × 3.14 =

*R= 14 cm

Answer 2

Given: The perimeters of a circular and square fields are equal. Area of the square field is 484 m square.

To find: Diameter of the circular field

Solution: Let each side of the square be a and radius of the circle be r.

Perimeter of the square field

= 4 × side

= 4a

Perimeter of the circular field

= 2πr

Since perimeter of circle and square are equal, therefore:

4a = 2πr

=> a = π×r/2

Now, area of square

= side × side

= a×a

But area of square field is 484 m square.

Therefore,

${a}^{2} = 484$

$= > a = \sqrt{484}$

$= > a = 22$

Therefore, a=22 m

Since, a = π ×r/2

=> 22 = (22/7)×r / 2 ( since π= 22/7)

=> 22 = 22×r / 7×2

=> 22 = 22r / 14

=> 22 × 14 = 22 r

=> r = 14 m

Diameter of the field

= 2 × radius

= 2×r

= 2×14

= 28 m

Therefore, the diameter of the circular field is 28 m.