What is the formula for the Pythagorean theorem?

The Pythagorean theorem 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 relationship is crucial in geometry and provides a way to determine a side length when the lengths of the other two sides are known.

The formula ( a² + b² = c² ) precisely captures this relationship, where ( c ) represents the length of the hypotenuse, while ( a ) and ( b ) denote the lengths of the two other sides. This means if you know the lengths of any two sides of a right triangle, you can use this formula to calculate the length of the third side.

For example, if one side is 3 units and another side is 4 units, you can calculate the hypotenuse as follows: ( 3² + 4² = c² ) leads to ( 9 + 16 = c² ), giving ( c² = 25 ) or ( c = 5 ). This demonstrates the theorem's practical application in solving real-world problems involving right triangles.

In contrast to the correct formula, the