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 squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side. Within a given triangle, a longer common side is associated with a smaller inscribed square. If an inscribed square has side of length "q" and the triangle has a side of length "a", part of which side coincides with a side of the square, then "q", "a", the altitude "h" from the side "a", and the triangle's area "T" are related according to The largest possible ratio of the area of the inscribed square to the area of the triangle