Right triangle altitude to the hypotenuse is related to the legs of the right triangle by For solutions of this equation in integer values of "a, b, f", and "c", see here. The altitude from either leg coincides with the other leg. Since these intersect at the right-angled vertex, the right triangle's orthocenter—the intersection of its three altitudes—coincides with the right-angled vertex. The Pythagorean theorem states that: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the
Fermat's right triangle theorem of a right triangle with square area. By dividing by any common factors, one can assume that this triangle is primitive and from the known form of all primitive Pythagorean triples, one can set formula_23, formula_24, and formula_25, by which the problem is transformed into finding relatively prime integers formula_26 and formula_27 (one of which is even) such that formula_28 is square. The four linear factors formula_26, formula_27, formula_31, and formula_32 are relatively prime and therefore must themselves be squares; let formula_33 and formula_34. Both formula_35 and formula_36 must be odd since exactly one of formula_26 or formula_27 is even