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Does there exist an equilateral triangle with sides \(27\), \(27\), \(27\)? In general, does there exist an equilateral triangle of any sidelength? Justify your answer.
Interpretation:
, an equilateral triangle with sides \(27\), \(27\), \(27\) exists because the sum of two sides is than the third side.
In an equilateral triangle, all sides are , so this condition is satisfied.
So, an equilateral triangle always exists for sidelength.
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