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# Triangle Inequality

The triangle inequality states that the sum of any two sides of a non-degenerate triangle must equal more than the third side. Thus a triangle with side lengths $$3, 4$$, and $$7$$ is not possible since $$3+4 \not > 7$$.

This property sets a boundary on the possible lengths of an unknown side of a given triangle. For example, if we know that a triangle has side lenghts of $$4, 8,$$, and $$x$$, we know that $$4 < x < 12$$ since if $$x \leq 4$$ it will be too short to satisfy the triangle inequality ( $$4 + x \not > 8$$ ), and if $$x \geq 12$$, then it will be too long, since $$4 + 8 = 12 \not > x$$.

Note by Arron Kau
2 years, 11 months ago