In a right triangle, the hypotenuse is the longest side, which is opposite the right angle. It can be measured against the lengths of the two legs of the triangle using the well-known Pythagorean theorem. This theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula can be expressed as:
c² = a² + b²
This means that the hypotenuse is not just longer than each leg, but its length is specifically related to the lengths of the legs in a precise mathematical relationship. For instance, if you know the lengths of both legs, you can determine the length of the hypotenuse. Conversely, if you have the hypotenuse and one leg, you can also find the length of the other leg. Thus, the hypotenuse is fundamentally tied to the legs through this relationship, further demonstrating that its length always exceeds those of the legs in a right triangle.