Chapter 8.10, Problem 1E

To determine

(a)

To explain:

The calculations in the given chart.

Step	Number of Triangles	Length of Each Side	Perimeter of One Triangle	Total Perimeter of All Triangles
1	$1$	$1\text{ft}$	$3\cdot 1\text{ft}=3\text{ft}$	$1\cdot 3\text{ft}=3\text{ft}$
2	$3$	$\begin{array}{l}1/2\cdot 1\text{ft}\\ =1/2\text{ft}\end{array}$	$\begin{array}{l}3\cdot 1/2\text{ ft}\\ =3/2\text{ft}\end{array}$	$\begin{array}{l}3\cdot 3/2\text{ ft}\\ =9/2\text{ft}\end{array}$
3
4
5
6

To determine

(b)

To find:

The remaining values in the given table.

To determine

(c)

The factor by which the number of triangles increases and explain the answer.

To determine

(d)

The factor by which the length of each side decreases and explain the answer.

To determine

(e)

The factor by which the perimeter of one triangle changes, explain the answer and determine if the perimeter of one triangle is increasing or decreasing.

To determine

(f)

The factor by which the total perimeter of all new triangles changes, explain the answer and determine if the total perimeter of all new triangles is increasing or decreasing.

To determine

(g)

To find:

The formula for the total perimeter of all new triangles at step $n$.

To determine

(h)

The perimeter of the Sierpinski gasket.