Does there exist an equilateral triangle with sides \(47\), \(47\), \(47\)? In general, does there exist an equilateral triangle of any sidelength? Justify your answer.
Interpretation:
, an equilateral triangle with sides \(47\), \(47\), \(47\) 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.