To determine the sets of side lengths of similar triangles to a triangle with side lengths of 3, 4, and 8 units, we need to look for sets that have proportional relationships with the given triangle. The ratio of corresponding sides of similar triangles should be equal.
Given triangle with side lengths 3, 4, and 8 units:
- Ratio of side lengths: 3:4:8
Now, let's analyze each set of side lengths provided:
1. 6, 8, 16
- Ratio: 6:8:16 = 3:4:8
- These side lengths are in proportion and form a similar triangle to the given triangle.
2. 5, 6, 10
- Ratio: 5:6:10 ≠ 3:4:8
- These side lengths are not in proportion to the given triangle and do not form a similar triangle.
3. 6, 7, 11
- Ratio: 6:7:11 ≠ 3:4:8
- These side lengths are not in proportion to the given triangle and do not form a similar triangle.
4. 9, 12, 24
- Ratio: 9:12:24 = 3:4:8
- These side lengths are in proportion and form a similar triangle to the given triangle.
5. 15, 20, 40
- Ratio: 15:20:40 = 3:4:8
- These side lengths are in proportion and form a similar triangle to the given triangle.
6. 12, 16, 28
- Ratio: 12:16:28 ≠ 3:4:8
- These side lengths are not in proportion to the given triangle and do not form a similar triangle.
Therefore, the sets of side lengths that are similar to the triangle with side lengths of 3, 4, and 8 units are:
- 6, 8, 16
- 9, 12, 24
- 15, 20, 40
