Why is the hypotenuse always longer than the legs?
Hypotenuse is located opposite to a bigger angle (the right angle measured at
See details below.
In any triangle sides, opposite to congruent angles, are congruent.
A side, opposite to a bigger angle, is bigger than a side that lies opposite to a smaller angle.
For a proof of these statements I can refer you to Unizor, menu items Geometry - Triangles - Sides & Angles.
The largest angle in a right triangle is the right angle, therefore, opposite to it lies the longest side - hypotenuse.