Geometry: Maximum or Minimum Perimeter?

[googoogaagaa]

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!

 

[lzkelley]

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...

 

[uman]

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.