With a square that has the same side length as a circle's perimeter radius, which is then largest?


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David Shabazi answered

Perimeter for a square: 4s (s = length of one side)

Perimeter(Circumference) of a circle: 2πr (r = radius)

If the side lengths are the same, then both perimeter formulas will use the same variable. So

2πr = 4r

2πr/2r = 4r/2r (Divide 2r from both sides)

π = 2 <--- This is false, since π is 3.14.

Since π is bigger than 2, the perimeter for a circle, the circumference, makes it so that the circle is larger than the square if they had the same side lengths. However, if you were talking about area...

Area of a square: S^2 (s = length of one side)

Area of a circle: πr^2 (r = radius)

Set them equal to each other

πr^2 = r^2

πr^2/r^2 = r^2/r^2 (Divide r^2 from both sides)

π = 1

In this case, it still says that π is lower than 3.14. We come to the same conclusion that the circle is larger than the square when both a side length and radius are the same.

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