What is the formula for the Pythagorean theorem?

The formula for the Pythagorean theorem is expressed as a² + b² = c², where 'a' and 'b' represent the lengths of the legs of a right triangle, and 'c' denotes the length of the hypotenuse, the side opposite the right angle. This theorem establishes a fundamental relationship in Euclidean geometry, as it allows the calculation of the length of one side of a right triangle when the lengths of the other two sides are known.

The significance of this formula lies in its application across various fields such as architecture, physics, and engineering, where determining distances and relationships within right triangles is essential. Thus, understanding and applying this theorem is critical in solving problems involving right triangles, confirming why the chosen answer accurately represents the Pythagorean theorem.