The hypotenuse is the longest side because of the definition. By definition, the hypotenuse is the side opposite of the right angle in the triangle. Because a triangle is only made of of 180deg, and the right angle is 90deg...no other angle can be larger than the right angle, hence no side can be longer than the side opposite the largest angle.The word derives from the Greek hypo- ("under") and teinein ("to stretch").
mathworld.wolfram.com