Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus it is a right triangle.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 28, so 7x = 28, giving x = 4. Thus, A's age = 3x = 12.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 70, giving 7x = 70, so x = 10. Thus, A's age = 3x = 30.

The sum of the first n natural numbers is given by the formula n(n + 1)/2 = 255. Solving n(n + 1) = 510, we find n = 16.

Expanding gives 2x - 6 = 8. Adding 6 gives 2x = 14, thus x = 7.

Adding 4 to both sides gives 2x = 14. Dividing by 2 gives x = 7.

Subtracting 8 from both sides gives 4x = 16. Dividing by 4 gives x = 4.

Calculating gives 2(7) - 5 = 14 - 5 = 9.

Calculating gives 4 × 5 - 5 = 20 - 5 = 15.

Subtracting 3 from both sides gives 2x = 12. Dividing by 2 gives x = 6.

Subtracting 5 from both sides gives 3x = 15. Dividing by 3 gives x = 5.

Adding 3 to both sides gives 5x = 5. Dividing by 5 gives x = 1.