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

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Senior Manager
Joined: 20 Feb 2007
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If the area of a square is equal to the area of a circle, [#permalink]  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?
Director
Joined: 05 Feb 2006
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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
Senior Manager
Joined: 20 Feb 2007
Posts: 257
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Thanks SimaQ, I was stuck here 2sqrt(pi)/pi.....
Manager
Joined: 28 Feb 2007
Posts: 197
Location: California
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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)
Senior Manager
Joined: 22 Jun 2006
Posts: 286
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techjanson, you're right
even i get the same ratio

peri of sq / circ of circle = 2 / (pi^2)
Manager
Joined: 15 Nov 2006
Posts: 224
Location: Ohio
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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)
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