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SainT -
post Sep 19 2007, 10:17 AM
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The question is as follows:

If the perimeter of a square and the circumference of a circle are the same, then which one of the two has a
smaller area? Explain your answer.

I have no clue where to begin, I am incline towards the circle. But Why?
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foxshox -
post Sep 19 2007, 05:06 PM
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Its going to be the circle..
the equation of perimeter for a square is S*4
the equation for a circumference of a circle is pi*d.

So to find the area of the square you need to square a side of it.
So its S^2. So the side of the square is = to P/4, and when you square it you get P^2/16 as the area.

Then we look at the circle. To find the radius of the circle( which you need for the area since A=pi*r^2), we have to divide the circumference by pi and then half that. So the radius is = to P/(2*pi). Then we have to square it and multiply it by pi. So we get (P^2 * pi)/(4*pi^2). We then cancel out to get P^2/(4*pi).

So we have to find which one is bigger P^2/16 or P^2/4*pi, and since 1/16 is less then 1/4*pi the circle is bigger.

This post has been edited by foxshox: Sep 19 2007, 05:07 PM
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SainT -
post Sep 19 2007, 09:05 PM
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QUOTE (foxshox @ Sep 19 2007, 07:06 PM)
Its going to be the circle..
the equation of perimeter for a square is S*4
the equation for a circumference of a circle is pi*d.

So to find the area of the square you need to square a side of it.
So its S^2. So the side of the square is = to P/4, and when you square it you get P^2/16 as the area.

Then we look at the circle. To find the radius of the circle( which you need for the area since A=pi*r^2), we have to divide the circumference by pi and then half that. So the radius is = to P/(2*pi). Then we have to square it and multiply it by pi. So we get (P^2 * pi)/(4*pi^2). We then cancel out to get P^2/(4*pi).

So we have to find which one is bigger P^2/16 or P^2/4*pi, and since 1/16 is less then 1/4*pi the circle is bigger.

I actually worked this out as well my friend but you are dead on, I had a feeling you'd be replyin to this one smile.gif
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Jager -
post Sep 20 2007, 09:31 AM
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Wow I guess if anyone has any math questions just pm foxshox instead of even posting lol.

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