A triangle having all sides of different lengths is called :

The correct option is A scalene triangle.

To understand why this is the correct answer, let us review the classification of triangles based on their side lengths:

1. Scalene Triangle: A triangle in which all three sides have different (unequal) lengths. Consequently, all three interior angles also have different measures.

2. Isosceles Triangle: A triangle that has at least two sides of equal length. The angles opposite to these equal sides are also equal.

3. Equilateral Triangle: A triangle in which all three sides are equal in length. All interior angles are equal as well, each measuring 60°.

4. Right Triangle: A triangle defined by having one internal angle equal to 90° (a right angle), regardless of side lengths.

Therefore, a triangle having all sides of different lengths is called a scalene triangle.