Geometry: Maximum or Minimum Perimeter?

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However, 4 is the greatest lower bound of the possible perimeters of the rectangle.In summary, mathematically, the maximum angle of a triangle with two legs of length 2 is 180 degrees, and the minimum perimeter of a rectangle with two opposite sides of length 2 is 4.
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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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  • #2
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...
 
  • #3
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.
 

What are the two basic geometry questions?

The two basic geometry questions are: "What is the area of a shape?" and "What is the perimeter of a shape?"

How do you find the area of a shape?

To find the area of a shape, you need to know the measurements of its sides. The formula for finding the area of a shape varies depending on the shape. For example, the formula for finding the area of a square is length x width, while the formula for finding the area of a triangle is 1/2 x base x height.

How do you find the perimeter of a shape?

To find the perimeter of a shape, you need to know the lengths of all its sides. The perimeter is the distance around the edge of the shape. To find the perimeter, you add up the lengths of all the sides.

What is the difference between area and perimeter?

Area is the measure of the surface inside a shape, while perimeter is the measure of the distance around the edge of a shape. In other words, area tells you how much space a shape takes up, while perimeter tells you how much distance you would cover if you walked around the shape.

Why are area and perimeter important in geometry?

Area and perimeter are important in geometry because they are fundamental concepts that are used to measure and describe shapes. They are also used in many real-life applications, such as calculating the amount of paint needed to cover a wall or the amount of fencing needed to enclose a garden.

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