QQuestionMathematics
QuestionMathematics
The side lengths 4, 8, and 12 can be used to form a triangle.
A. True
B. False
12 months agoReport content
Answer
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Step 1:I'll solve this step by step using the specified LaTeX formatting guidelines:
Step 2:: Check Triangle Inequality Theorem
The Triangle Inequality Theorem states that for three side lengths to form a triangle, the sum of any two sides must be greater than the third side. Let's check each combination: - 4 + 8 = 12 (equal to the third side, not strictly greater) - 4 + 12 = 16 > 8 ✓ - 8 + 12 = 20 > 4 ✓
Step 3:: Detailed Analysis
While two of the conditions are satisfied, the first condition (4 + 8 = 12) means these lengths cannot form a triangle. For a triangle to exist, the sum of any two sides must be strictly greater than the third side.
Step 4:: Conclusion
Since 4 + 8 = 12, which does not satisfy the triangle inequality strictly, these side lengths cannot form a triangle.
Final Answer
False Explanation: The side lengths 4, 8, and 12 fail the triangle inequality theorem because the sum of the two shorter sides (4 + 8) is equal to the longest side (12), which means these lengths cannot form a closed triangle.
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