Question

Question
Which set of side lengths will form a triangle? All measurements are in feet.(1 point)
Responses

3, 3, 6
3, 3, 6

4, 1, 6
4, 1, 6

5, 2, 4
5, 2, 4

8, 6, 2

Answer 1

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

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

Let's check each set of side lengths:

1. **3, 3, 6**:
- \( 3 + 3 > 6 \) (False)
- Since the first condition is false, these cannot form a triangle.

2. **4, 1, 6**:
- \( 4 + 1 > 6 \) (False)
- Since the first condition is false, these cannot form a triangle.

3. **5, 2, 4**:
- \( 5 + 2 > 4 \) (True)
- \( 5 + 4 > 2 \) (True)
- \( 2 + 4 > 5 \) (True)
- All conditions are true, so these can form a triangle.

4. **8, 6, 2**:
- \( 8 + 6 > 2 \) (True)
- \( 8 + 2 > 6 \) (True)
- \( 6 + 2 > 8 \) (False)
- Since the third condition is false, these cannot form a triangle.

Therefore, the only set of side lengths that can form a triangle is **5, 2, 4**.