Geometry: Maximum or Minimum Perimeter?

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The discussion centers on the mathematical properties of triangles and rectangles regarding their perimeters. For a triangle with two legs of length 2, the maximum perimeter approaches 8, with 7.999... being the least upper bound. In the case of a rectangle with two opposite sides of length 2, the minimum perimeter approaches 4, with 4.00000... being the limit. The conclusion is that neither shape has a defined maximum or minimum perimeter, but rather, they have least upper bounds.

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If a triangle has two legs with lengths of 2 each, is the maximum permiter of that triangle 8, or 7.999 (repeating)? In other words, is the maximum angle of a triangle 180 degrees, or 17.999 (repeating) degrees?

Also, if a rectangle has two opposite sides with lengths of 2, is the minimum permiter of that rectangle 4, or 4.000000...1 (approching 4)?

Thank you!
 
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Mathematically its not too hard to prove (using infinite an series) that 7.9999... (on indefinitely) is the same as 8. Similarly for 4.00000...
 
In the first case, there is no maximum perimeter; however, 8 is the least upper bound of the possible perimiters of the triangle.

The second case is similar: no minimum perimeter.
 

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