The triangle inequality theorem states that for three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's denote the sides as:
- \( a = 3 \) feet
- \( b = 4 \) feet
- \( c = 5 \) feet
We need to check the following conditions:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
Now, let's check each condition:
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Check \( a + b > c \): \[ 3 + 4 > 5 \implies 7 > 5 \quad \text{(True)} \]
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Check \( a + c > b \): \[ 3 + 5 > 4 \implies 8 > 4 \quad \text{(True)} \]
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Check \( b + c > a \): \[ 4 + 5 > 3 \implies 9 > 3 \quad \text{(True)} \]
Since all three conditions are true, the sides with lengths of 3 feet, 4 feet, and 5 feet do indeed form a triangle according to the triangle inequality theorem.
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