Question

Which set of side lengths will form a triangle? All measurements are in feet.(1 point)Responses8, 6, 28, 6, 24, 1, 64, 1, 63, 3, 63, 3, 65, 2, 4

Answer 1

To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem, which 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 provided side lengths:

1. **8, 6, 28**
- \( 8 + 6 = 14 \) which is not greater than 28 (fails)

2. **6, 24, 1**
- \( 6 + 1 = 7 \) which is not greater than 24 (fails)

3. **64, 1, 63**
- \( 64 + 1 = 65 \) which is greater than 63 (passes)
- \( 64 + 63 = 127 \) which is greater than 1 (passes)
- \( 1 + 63 = 64 \) which is not greater than 64 (fails)

4. **3, 63, 3**
- \( 3 + 3 = 6 \) which is not greater than 63 (fails)

5. **65, 2, 4**
- \( 65 + 2 = 67 \) which is greater than 4 (passes)
- \( 65 + 4 = 69 \) which is greater than 2 (passes)
- \( 2 + 4 = 6 \) which is not greater than 65 (fails)

In conclusion, none of the provided sets of side lengths can form a triangle. Each set fails at least one part of the triangle inequality theorem.