Final answer:
In a Pythagorean triple, at least one leg of the triangle must have an even-numbered length because when you square an odd number, the result is always odd.
Step-by-step explanation:
In a Pythagorean triple, which consists of three positive integers (a, b, c) that satisfy the equation a² + b² = c², at least one leg of the triangle must have an even-numbered length.
This is because when you square an odd number, the result is always odd. However, when you square an even number, the result is always even. Therefore, the only way for the sum of two squares to equal another square is if at least one of the squares is even.
For example, in the Pythagorean triple (3, 4, 5), both 3 and 4 are odd, but the sum of their squares (9 + 16 = 25) equals the square of the hypotenuse, which is 5 (an odd number).