Question

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

पर्याय

• 22 : 7    

• 13 : 22

• 14 : 11       

• 7 : 22 

• 22 : 13

• 11 : 14

Answer 1

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11.

Explanation:

Let radius of circle be r and side of a square be a.

According to the given condition,

Perimeter of a circle = Perimeter of a square

∴ 2πr = 4a

⇒ a = `(π"r")/2`  ...(i)

Now, `"Area of circle"/"Area of square"`

= `(π"r"^2)/("a")^2`

= `(π"r"^2)/((π"r")/2)^2`  ...[From equation (i)]

= `(π"r"^2)/((π^2"r"^2)/4)`

= `4/π`

= `4/(22/7)`

= `28/22`

= `14/11`