The sum of the squares of three numbers is 280. If these numbers are in the ratio 3:5:6, what is the largest number?

Explanation

Let the three numbers be 3x, 5x, and 6x. According to the problem, (3x)² + (5x)² + (6x)² = 280, which simplifies to 9x² + 25x² + 36x² = 280, or 70x² = 280. Solving for x² gives x² = 4, so x = 2. The greatest number is therefore 6x = 6 × 2 = 12.