The longest side of a right triangle is called the hypotenuse. To understand why the hypotenuse is the longest side, let's first review what a right triangle is and its properties.

A right triangle is a triangle that has one angle measuring 90 degrees. This angle is called the right angle. The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees.

Now, let's explore the properties of a right triangle that help us identify the longest side:

1. Right Angle (90 degrees):
- The right angle is formed by the intersection of the two shorter sides of the triangle.
- It is always the largest angle in a right triangle.

2. Legs:
- The two shorter sides of the right triangle that form the right angle are called the legs.
- The lengths of the legs can vary.

3. Hypotenuse:
- The side opposite the right angle is called the hypotenuse.
- It is the longest side in a right triangle.
- The length of the hypotenuse is determined by the lengths of the legs.

To understand why the hypotenuse is the longest side, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

Mathematically, it can be represented as:

c^2 = a^2 + b^2

Where c represents the length of the hypotenuse, and a and b represent the lengths of the legs.

Since the hypotenuse is squared in the equation, its value will always be greater than the square of either leg. Therefore, the hypotenuse is always longer than either of the two legs.

In conclusion, the hypotenuse is the longest side of a right triangle because of the properties of right triangles and the mathematical relationship expressed by the Pythagorean theorem.