Question

Which set of side lengths will form a triangle? All lengths are given in meters.(1 point)
Responses

26, 12, 12
26, 12, 12

50, 60, 26
50, 60, 26

50, 30, 80
50, 30, 80

60, 26, 33

Answer 1

To determine if a 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 \( c \):

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

We will evaluate each set of side lengths against these conditions.

1. **For 26, 12, 12:**
- \( 26 + 12 > 12 \) (True)
- \( 26 + 12 > 12 \) (True)
- \( 12 + 12 > 26 \) (False)

This set does **not** form a triangle.

2. **For 50, 60, 26:**
- \( 50 + 60 > 26 \) (True)
- \( 50 + 26 > 60 \) (True)
- \( 60 + 26 > 50 \) (True)

This set **forms** a triangle.

3. **For 50, 30, 80:**
- \( 50 + 30 > 80 \) (False)

This set does **not** form a triangle.

4. **For 60, 26, 33:**
- \( 60 + 26 > 33 \) (True)
- \( 60 + 33 > 26 \) (True)
- \( 26 + 33 > 60 \) (False)

This set does **not** form a triangle.

**Conclusion:** The only set of side lengths that will form a triangle is **50, 60, 26**.