Using the triangle inequality theorem, the set of lengths that meet all the requirement is: 3, 4, 5, 7.
What is the Triangle Inequality Theorem?
The triangle inequality theorem states that the sum of any of the two sides of a triangle must be equal or greater than the third side, i.e. if a, b, and c are sides of a triangle, then:
- a + b ≥ c
- b + c ≥ a
- a + c ≥ b
If we have the following set of numbers, 3, 4, 5, 7.
Set 3, 4, 5 will give us:
- 3 + 4 ≥ 5
- 4 + 5 ≥ 3
- 3 + 4 ≥ 5
This means 3, 4, 5 will form a triangle.
Set 4, 5, 7 will give us:
- 4 + 5 ≥ 7
- 5 + 7 ≥ 4
- 7 + 4 ≥ 5
This means 4, 5, 7 will form a triangle.
Set, 3, 5, 7 will give us:
- 3 + 5 ≥ 7
- 5 + 7 ≥ 3
- 7 + 3 ≥ 5
This means 3, 5, 7 will form a triangle.
Set 3, 4, 7 will give us:
- 3 + 4 ≥ 7
- 4 + 7 ≥ 3
- 7 + 3 ≥ 4
This means 3, 4, 7 will form a triangle.
Therefore, we can conclude that the set of lengths, 3, 4, 5, 7, meets all the requirements.
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