Question

Which set of side lengths will form a triangle? All lengths are given in meters.

60, 26, 33

50, 30, 80

26, 12, 12

50, 60, 26

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 side lengths \(a\), \(b\), and \(c\), the following conditions must be met:

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

Let's check each set of side lengths:

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

Therefore, **this set does not form a triangle.**

2. **50, 30, 80**:
- \(50 + 30 = 80 \not> 80\) (False)

Therefore, **this set does not form a triangle.**

3. **26, 12, 12**:
- \(26 + 12 = 38 > 12\) (True)
- \(26 + 12 = 38 > 12\) (True)
- \(12 + 12 = 24 < 26\) (False)

Therefore, **this set does not form a triangle.**

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

Therefore, **this set does form a triangle.**

In conclusion, the only set of lengths that can form a triangle is **50, 60, 26**.