Which side is always the longest in a right triangle?

In a right triangle, the hypotenuse is always the longest side. This is because the hypotenuse is the side opposite the right angle and, according to the Pythagorean theorem, it is subjected to a unique relationship with the other two sides (the adjacent and opposite sides). The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, by mathematical necessity, the hypotenuse must be longer than either of the other two sides in a right triangle.

The adjacent side and the opposite side can vary in length but cannot each exceed the length of the hypotenuse. This fundamental property is what distinguishes right triangles and is essential for solving problems involving them.