Triangle Inequality Calculator
Determine whether three side lengths can form a valid triangle, classify it by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse), and compute the area and perimeter.
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. If a + b > c, a + c > b, and b + c > a all hold, the three lengths form a valid triangle. If any condition fails, no triangle is possible.
Triangles are classified by sides: equilateral (all three sides equal), isosceles (exactly two sides equal), and scalene (all sides different). They are also classified by angles: acute (all angles less than 90°), right (one angle exactly 90°), and obtuse (one angle greater than 90°). The angle classification can be determined without computing angles by comparing c² (the longest side squared) with a² + b²: if equal, it is right; if less, acute; if greater, obtuse.
The area of a triangle when all three sides are known is calculated using Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s = (a + b + c) / 2 is the semi-perimeter. This elegant formula avoids needing to know any angles.