math

posted by .

you start with an equilateral triangle and then trisect each of the sides with a new equilateral triangle on the middle third of each trisection, repeat the process indefinitely
how would you prove that the perimeter is infinite?

  • math -

    You start out with three sides of length a, and the figure perimeter is 3a.

    After the first step you described, you have a figure with 12 sides of length a/3. The perimeter is now 4a.

    After a similar second step, you will have 48 sides of length a/9. The perimeter is now 5.33 a

    After N such steps, you have 3*4^N sides of length a/3^N, with a perimeter of = 3a*(4/3)^N

    That number clearly becomes infinite as N becomes infinite

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    A pentagon is formed by putting together three identical equilateral triangles and one larger equilateral triangle with length of edge equal to 2 times that of the smaller equilateral triangle. If the perimeter of the smaller triangle …
  2. Algebra

    The perimeter of an equilateral triangle is 7 in. more than the perimeter of a square. The side of the triangle is 5 in. longer than the side of the square. Find the length of each side of the triangle. (Note: An equilateral triangle …
  3. geometry

    Rewrite the statement in if-then form. All equilateral triangles have three congruent sides. a. a figure has three congruent sides if and only if it is an equilateral triangle. b. a figure is an equilateral triangle if and only if …
  4. math

    An equilateral triangle has a perimeter of 33 inches. What would the perimeter of a square whose sides each measure the same length as the side of the triangle?
  5. math

    The perimeter of a square piece of land is twice the perimeter of an equilateral triangle. (an equilateral triangle has three equal sides.) If one side of the square is 45 feet, find the length of the sides of the triangle. 2x + 3 …
  6. math

    If an equithagorean triangle is an equilateral triangle in which the sum of the cubes of two sides is equal to the square of the third side, what is the perimeter of an equithagorean triangle?
  7. Algebra 2

    Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the sum of a finite geometric series. The sides of an equilateral triangle measure 16 inches. The midpoints of the sides …
  8. math

    The large red equilateral triangle has sides of 8x units. The midpoints of the red triangle are joined to form the blue triangle. The midpoints of the blue triangle ate joined to form the green triangle. The process of joining midpoints …
  9. math

    The large red equilateral triangle has sides of 8x units. The midpoints of the red triangle are joined to form the blue triangle. The midpoints of the blue triangle ate joined to form the green triangle. The process of joining midpoints …
  10. math

    The large red equilateral triangle has sides of 8x units. The midpoints of the red triangle are joined to form the blue triangle. The midpoints of the blue triangle ate joined to form the green triangle. The process of joining midpoints …

More Similar Questions