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That should not surprise you. Here's a thought that might make you more comfortable with it:

-- Take a good sized piece of string.

Tie the ends together.

-- Now you have a big limp loop.

Drop it down on the ground.

-- How many different shapes can you make out of it ? A square ? A circle ?

Different short fat rectangles ? Triangles ? Different long skinny rectangles ?

Odd-ball shapes with 9 sides or 17 sides ? Shapes with some straight sides

and some curved sides ?

You can push the string loop around into millions of different shapes. The string loop

is the perimeter of every one of them.

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12y ago

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Q: How does different shapes have the same perimeter?
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