Question

which set of side lengths will form a triangle? all lengths are given in meters.

60 26 33.

26 12 12.

50 30 80.

50 60 26.

Answer 1

To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem. The theorem states that for three lengths \(a\), \(b\), and \(c\), the following conditions must be satisfied:

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

Let's apply this rule to each set of side lengths.

1. **Lengths: 60, 26, 33**
- \(60 + 26 > 33 \) → \(86 > 33\) (True)
- \(60 + 33 > 26 \) → \(93 > 26\) (True)
- \(26 + 33 > 60 \) → \(59 > 60\) (False)

This set does NOT form a triangle.

2. **Lengths: 26, 12, 12**
- \(26 + 12 > 12 \) → \(38 > 12\) (True)
- \(26 + 12 > 12 \) → \(38 > 12\) (True)
- \(12 + 12 > 26 \) → \(24 > 26\) (False)

This set does NOT form a triangle.

3. **Lengths: 50, 30, 80**
- \(50 + 30 > 80 \) → \(80 > 80\) (False)
- \(50 + 80 > 30 \) → \(130 > 30\) (True)
- \(30 + 80 > 50 \) → \(110 > 50\) (True)

This set does NOT form a triangle.

4. **Lengths: 50, 60, 26**
- \(50 + 60 > 26 \) → \(110 > 26\) (True)
- \(50 + 26 > 60 \) → \(76 > 60\) (True)
- \(60 + 26 > 50 \) → \(86 > 50\) (True)

This set DOES form a triangle.

**Summary**:
- The side lengths **50, 60, 26** can form a triangle.
- The other sets of lengths cannot form a triangle.