Which of the following represents the Pythagorean theorem?

The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. Specifically, it states that 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.

In mathematical terms, if we denote the lengths of the two legs of the triangle as 'a' and 'b', and the length of the hypotenuse as 'c', the correct representation of the theorem is given by the equation where the squares of 'a' and 'b' are added together to equal the square of 'c'. This is expressed as ( a^2 + b^2 = c^2 ).

This formula is instrumental for solving many problems in geometry, including finding the lengths of sides when two sides are known, and it can also be applied in various real-world scenarios involving right triangles. Understanding this theorem is vital not only in mathematics but also in fields like physics, engineering, and architecture.