What classification applies to a triangle with no sides of equal length?

A triangle with no sides of equal length is classified as scalene. In a scalene triangle, all three sides are of different lengths, which also means that all three angles are different. This distinguishes it from other types of triangles.

An isosceles triangle, for example, specifically has at least two sides that are equal in length, which does not apply here. An equilateral triangle has all three sides and angles equal, so that classification also does not fit. A right triangle is defined by having one angle that measures exactly 90 degrees, and it can be isosceles or scalene, but is not exclusively defined by the lengths of its sides.

Therefore, the correct classification for a triangle with no sides of equal length is scalene, as it accurately describes a triangle where all sides and angles vary independently.