Question

which side lengths could not form a triangle
1. 5m, 6m, 8m
2. 10m,10m,2m
3. 19m ,34m,15m
4. 3m ,16m, 14m

Answer 1

To determine whether a set of lengths can form a triangle, we can use the triangle inequality theorem, which states that for any triangle with side lengths \(a\), \(b\), and \(c\):

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

If any of these conditions are violated, the lengths cannot form a triangle.

Now, let's check each set of lengths:

1. **5m, 6m, 8m:**
- \(5 + 6 = 11 > 8\) (true)
- \(5 + 8 = 13 > 6\) (true)
- \(6 + 8 = 14 > 5\) (true)
- **This set can form a triangle.**

2. **10m, 10m, 2m:**
- \(10 + 10 = 20 > 2\) (true)
- \(10 + 2 = 12 > 10\) (true)
- \(10 + 2 = 12 > 10\) (true)
- **This set can form a triangle.**

3. **19m, 34m, 15m:**
- \(19 + 34 = 53 > 15\) (true)
- \(19 + 15 = 34 > 34\) (false, equal)
- \(34 + 15 = 49 > 19\) (true)
- **This set cannot form a triangle** because \(19 + 15\) is not greater than \(34\).

4. **3m, 16m, 14m:**
- \(3 + 16 = 19 > 14\) (true)
- \(3 + 14 = 17 > 16\) (true)
- \(16 + 14 = 30 > 3\) (true)
- **This set can form a triangle.**

### Summary:
The only set that cannot form a triangle is **19m, 34m, 15m**.