Question

Which set of side lengths will form a triangle? All measurements are in feet.(1 point) Responses 8, 6, 2 8, 6, 2 5, 2, 4 5, 2, 4 4, 1, 6 4, 1, 6 3, 3, 6

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 sides of lengths \( a \), \( b \), and \( c \), the following must be true:

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

Let's check each set of side lengths:

1. **8, 6, 2**
- \( 8 + 6 > 2 \) → \( 14 > 2 \) (true)
- \( 8 + 2 > 6 \) → \( 10 > 6 \) (true)
- \( 6 + 2 > 8 \) → \( 8 > 8 \) (false)
- **Cannot form a triangle**

2. **5, 2, 4**
- \( 5 + 2 > 4 \) → \( 7 > 4 \) (true)
- \( 5 + 4 > 2 \) → \( 9 > 2 \) (true)
- \( 2 + 4 > 5 \) → \( 6 > 5 \) (true)
- **Can form a triangle**

3. **4, 1, 6**
- \( 4 + 1 > 6 \) → \( 5 > 6 \) (false)
- **Cannot form a triangle**

4. **3, 3, 6**
- \( 3 + 3 > 6 \) → \( 6 > 6 \) (false)
- **Cannot form a triangle**

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