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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
Solution
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.
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