Which of the following is an example of the Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in geometry that describes the relationship between the lengths of the sides of a right triangle. It specifically states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is expressed mathematically as a² + b² = c², where 'a' and 'b' represent the lengths of the legs of the triangle, and 'c' represents the length of the hypotenuse.

In this case, the equation a² + b² = c² correctly encapsulates this relationship, demonstrating how to calculate the length of one side of a right triangle if the lengths of the other two sides are known. This theorem is widely applicable in various fields, including physics, engineering, and architecture, making it an essential concept in mathematics.

The other options presented do not represent the Pythagorean theorem and illustrate different mathematical concepts that do not pertain to the properties of right triangles.