Calculate the triangle's area given side lengths a = 1m, b = 2m, and c = 3m.
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Answer: A. 0 sq m
Explanation
The triangle inequality theorem requires the sum of any two sides exceeding the third. Adding side length one to side length two results in a sum equal to three. Because one plus two equals three the geometric condition fails meaning no triangle exists. A valid geometric triangle must satisfy three distinct side length inequality conditions simultaneously. Degenerate triangles collapse into straight lines when two shorter sides equal the longest side. Geometric shapes with zero area possess no internal space and cannot enclose any surface.
Structural engineers check side length constraints to ensure stability in trusses and framework designs. Computer graphics algorithms test geometric validity before rendering complex multi-sided polygonal mesh structures. Understanding degenerate shapes prevents mathematical errors in advanced geometry and spatial analysis. Option B suggests three square meters which incorrectly assumes any three numbers form a triangle. Option C suggests two square meters which ignores fundamental geometric rules regarding side lengths. Option D suggests six square meters which is physically impossible given the provided side dimensions.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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