Geometry: Maximum or Minimum Perimeter?

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In the discussion, it is established that for a triangle with two legs of length 2, the maximum perimeter is not definitively 8 but is instead 7.999... (repeating), which is mathematically equivalent to 8 as it represents the least upper bound. The maximum angle of a triangle cannot reach 180 degrees, reinforcing the idea that no maximum perimeter exists. Similarly, for a rectangle with two opposite sides of length 2, the minimum perimeter is not strictly 4 but approaches 4, indicating that there is no minimum perimeter. Both cases illustrate the concept of limits in geometry, emphasizing that while values can approach certain bounds, they do not necessarily attain them.
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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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