The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 5000. The sum of the numbers is:

Question: The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 5000. The sum of the numbers is-

Solution:
Let, the number be 3x, 4x, 5x

According to the question,
(3x)² + (4x)² + (5x)² = 5000
⇒ 9x² + 16x² + 25x² = 5000
⇒ 50x² = 5000
⇒ x² = 5000/50
⇒ x² = 100
∴ x = 10

∴ The sum of the numbers = 3x + 4x + 5x
= 30 + 40 + 50
= 120