Final answer:
An equiangular triangle cannot exist with sides of different lengths; the statement is false.
Step-by-step explanation:
An equiangular triangle, by definition, has all three interior angles equal, and because the sum of the angles in any triangle is 180 degrees, each angle in an equiangular triangle is 60 degrees. However, having equal angles does not dictate that the lengths of the sides have to be equal. In fact, it is impossible for a triangle to have three equal angles and sides of different lengths; such a triangle does not exist. Therefore, the statement 'An equiangular triangle has three sides with different lengths' is false.