Question

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

Answer 1

To determine whether a set of side lengths can form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any three sides \( a \), \( b \), and \( c \), the following conditions must be satisfied:

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

Let's evaluate each set of side lengths:

1. **4, 1, 6**:
- \( 4 + 1 = 5 \) (not greater than 6)
- \( 4 + 6 = 10 > 1 \)
- \( 1 + 6 = 7 > 4 \)
- **This set does not form a triangle.**

2. **5, 2, 4**:
- \( 5 + 2 = 7 > 4 \)
- \( 5 + 4 = 9 > 2 \)
- \( 2 + 4 = 6 > 5 \)
- **This set forms a triangle.**

3. **3, 3, 6**:
- \( 3 + 3 = 6 \) (not greater than 6)
- \( 3 + 6 = 9 > 3 \)
- \( 3 + 6 = 9 > 3 \)
- **This set does not form a triangle.**

4. **8, 6, 2**:
- \( 8 + 6 = 14 > 2 \)
- \( 8 + 2 = 10 > 6 \)
- \( 6 + 2 = 8 \) (not greater than 8)
- **This set does not form a triangle.**

In summary, the only set of side lengths that forms a triangle is **5, 2, 4**.