Question

A sequence represents the total length of the line segments in each of a series of figures. Starting with a line of length 9 feet, each successive figure is drawn by trisecting every line segment, leaving out the center section, and replacing it with the other two sides of an equilateral triangle. Use the table to find the pattern and fill in the missing total lengths in the table. Round to the nearest tenth.

Answer 1

Table:

| Figure # | Line Segment Length (ft) | Total Length (ft) |

| --- | --- | --- |

| 1 | 9 | 9 |

| 2 | 6 + 3 = 9 | 12 |

| 3 | 4 + 4 + 1 = 9 | 14 |

| 4 | 3 + 3 + 2 + 1 = 9 | 15 |

| 5 | 2 + 2 + 2 + 1 + 1 = 9 | 17 |

Answer:

The pattern in the table is that each successive figure has a total length of 9 feet, but the line segment lengths are calculated by adding the lengths of the two side segments of an equilateral triangle. To determine the total length of each figure, we can simply add the three line segment lengths.

Total Length of Figure #1: 9 feet

Total Length of Figure #2: 12 feet (6 + 3 + 3)

Total Length of Figure #3: 14 feet (4 + 4 + 1)

Total Length of Figure #4: 15 feet (3 + 3 + 2 + 1)

Total Length of Figure #5: 17 feet (2 + 2 + 2 + 1 + 1)

Total Length of Each Figure: 9 feet

Explanation: