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Original Question
Hal has three pieces of wood. Board A is 4 inches long, board B is 6 inches long, and board C is 12 inches long. If the full le...Question
Peter has three pieces of wood. Board A is 7 inches long, board B is 14 inches long, and board C is 5 inches long. If the full length of each board is used, can the three pieces of wood be placed together to form a triangle?
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GPT 3.5
To determine if the three pieces of wood can form a triangle, we must apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's consider all possible combinations of two boards:
1. Board A and Board B: 7 + 14 = 21 inches (greater than Board C)
2. Board A and Board C: 7 + 5 = 12 inches (greater than Board B)
3. Board B and Board C: 14 + 5 = 19 inches (greater than Board A)
Based on our calculations, all three combinations meet the criteria of the triangle inequality theorem, so the three pieces of wood can be placed together to form a triangle.
In this case, let's consider all possible combinations of two boards:
1. Board A and Board B: 7 + 14 = 21 inches (greater than Board C)
2. Board A and Board C: 7 + 5 = 12 inches (greater than Board B)
3. Board B and Board C: 14 + 5 = 19 inches (greater than Board A)
Based on our calculations, all three combinations meet the criteria of the triangle inequality theorem, so the three pieces of wood can be placed together to form a triangle.
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