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If the area of a square is equal to the area of a circle,

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Senior Manager
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If the area of a square is equal to the area of a circle, [#permalink] New post 14 Mar 2007, 02:02
If the area of a square is equal to the area of a circle, what will be the ratio of perimeter of the square to circumference of the circle?
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 [#permalink] New post 14 Mar 2007, 02:08
x^2=pir^2
x=sqrt(pir^2)
x=r*sqrt(pi)

What is the ratio of:
4x/2pir.....plug in x value

4r*sqrt(pi)/2pir
2sqrt(pi)/pi.....raise by ^2 numerator and denominator
4pi/pi^2
4/pi
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 [#permalink] New post 14 Mar 2007, 02:17
Thanks SimaQ, I was stuck here 2sqrt(pi)/pi.....
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 [#permalink] New post 14 Mar 2007, 12:16
SimaQ wrote:
x^2=pir^2
x=sqrt(pir^2)
x=r*sqrt(pi)

What is the ratio of:
4x/2pir.....plug in x value

4r*sqrt(pi)/2pir
2sqrt(pi)/pi.....raise by ^2 numerator and denominator
4pi/pi^2
4/pi


why we need to square?
Shouldn't the answer be just 2 /sqrt(pi) ?
We are asked ratio. a/b is not same as (a/b * a/b)
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 [#permalink] New post 23 Mar 2007, 02:22
techjanson, you're right
even i get the same ratio

peri of sq / circ of circle = 2 / (pi^2)
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 [#permalink] New post 23 Mar 2007, 14:07
et r be the radius of circle. a be the side of square.
pi*r^2=a^2
or a^2/r^2=pi
or a/r=sqrt(pi)

Now perimeter of square/perimeter of circle
= 4a/2*pi*r
=(2/pi)*(a/r)
=(2/pi)*sqrt (pi)
multiplying the numerator and denominator by sqrt(pi) and simplifying
perimeter of square/perimeter of circle=2/sqrt(pi)
  [#permalink] 23 Mar 2007, 14:07
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