Question

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Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent
the sides of a triangle. Can you make a triangle with these three objects? Use the
Triangle Inequality Theorem explain why or why not.
Measurements of each object

Answer 1

1. Three sticks of varying lengths (6 inches, 8 inches, 10 inches)
2. Three ropes of varying lengths (12 inches, 14 inches, 16 inches)
3. Three pencils of varying lengths (4 inches, 5 inches, 6 inches)

Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For the sticks:
- 6 inches + 8 inches = 14 inches, which is greater than 10 inches (10 < 14)
- 6 inches + 10 inches = 16 inches, which is greater than 8 inches (8 < 16)
- 8 inches + 10 inches = 18 inches, which is greater than 6 inches (6 < 18)

Therefore, the sticks can form a triangle.

For the ropes:
- 12 inches + 14 inches = 26 inches, which is greater than 16 inches (16 < 26)
- 12 inches + 16 inches = 28 inches, which is greater than 14 inches (14 < 28)
- 14 inches + 16 inches = 30 inches, which is greater than 12 inches (12 < 30)

Therefore, the ropes can form a triangle.

For the pencils:
- 4 inches + 5 inches = 9 inches, which is not greater than 6 inches (6 > 9)
- 4 inches + 6 inches = 10 inches, which is not greater than 5 inches (5 > 10)
- 5 inches + 6 inches = 11 inches, which is greater than 4 inches (4 < 11)

Therefore, the pencils cannot form a triangle.