scalene

Scalene is a term used primarily in geometry to describe a triangle in which all three side lengths are different. The word derives from Latin scalēnus, from Greek skalenos, meaning uneven or unequal.

In a scalene triangle, no two sides are equal, and consequently all three interior angles are distinct as well. By the contrapositive, if two angles were equal, the sides opposite them would be equal, which would make the triangle isosceles rather than scalene. Scalene triangles can be acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), or right-angled (one angle exactly 90 degrees). A common example of a scalene right triangle is the 3-4-5 triangle.

Key properties include the following: the largest angle lies opposite the longest side, and the shortest angle lies opposite the shortest side. The area of a scalene triangle can be found using Heron's formula when all three side lengths are known, or more directly via the formula (1/2)ab sin(C) when two sides and the included angle are known.

In broader usage, scalene can describe polygons whose sides are all of different lengths, though the term is most commonly applied to triangles. Scalene triangles are contrasted with isosceles triangles (two equal sides) and equilateral triangles (three equal sides).