Integer triangle rational formula_14 where formula_15 reduces the generated Heronian triangle to its primitive and formula_16 scales up this primitive to the required size. A Pythagorean triangle is right angled and Heronian. Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. All Pythagorean triples formula_17 with hypotenuse formula_18 which are primitive (the sides having no common factor) can be generated by where "m" and "n" are coprime integers and one of them is even with "m" > "n". Every even number greater than 2 can be the leg of a Pythagorean triangle (not necessarily primitive)
Triangle inequality that the longest side length is less than the semiperimeter. A mathematically equivalent formulation is that the area of a triangle with sides "a", "b", "c" must be a real number greater than zero. Heron's formula for the area is In terms of either area expression, the triangle inequality imposed on all sides is equivalent to the condition that the expression under the square root sign be real and greater than zero (so the area expression is real and greater than zero). The triangle inequality provides two more interesting constraints for triangles whose sides are "a, b, c", where "a