Question

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

Options

• 4 : π

• π : 4

• π : 7

• 7 : π

Answer 1

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is π : 4.

Explanation:

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

Now, Perimeter of circle = Circumference of the circle

⇒ 4a = 2π

`=>"a"/"r" = pi/2`

`=>"a"/2 = pi/2`

Now,

`("Area of square")/("Area of circle") = "a"^2/(pi"r"^2")`

`=1/pi xx ("a"/"r")^2`

`=1/pixxpi^2/4`

`=pi/4`

Hence, the correct answer is option π : 4.