To determine which sets of numbers can represent the sides of a triangle, we need to use the triangle inequality theorem. The theorem states that for any three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. We will apply this rule to each of the given sets of numbers.
### Set 1: {11, 21, 33}
- 11 + 21 = 32
- 11 + 33 = 44
- 21 + 33 = 54
Check:
- 32 is not greater than 33
Since 11 + 21 is not greater than 33, this set does not form a triangle.
### Set 2: {8, 20, 29}
- 8 + 20 = 28
- 8 + 29 = 37
- 20 + 29 = 49
Check:
- 28 is not greater than 29
Since 8 + 20 is not greater than 29, this set does not form a triangle.
### Set 3: {4, 14, 19}
- 4 + 14 = 18
- 4 + 19 = 23
- 14 + 19 = 33
Check:
- 18 is not greater than 19
Since 4 + 14 is not greater than 19, this set does not form a triangle.
### Set 4: {14, 23, 36}
- 14 + 23 = 37
- 14 + 36 = 50
- 23 + 36 = 59
Check:
- 37 is greater than 36
- 50 is greater than 23
- 59 is greater than 14
Since all conditions of the triangle inequality theorem are satisfied, this set forms a triangle.
Therefore, the correct set of numbers that can represent the three sides of a triangle is:
- {14, 23, 36}
