Three numbers are in the ratio 3:4:5. The sum of their squares is 1250. What is the sum of numbers?

Given:- Ratio = 3 : 4 : 5 and sum of their square = 1250

Now,

Let, x be the constant ratio

Therefore,

Ratio = 3x : 4x : 5x

As given in question,

Sum of Ratio squares = 1250

⇒ (3x)² + (4x)² + (5x)² = 1250

⇒ 9x² + 16x² + 25x² = 1250

⇒ 50x² = 1250

⇒ x² = 1250 ÷ 50

⇒ x² = 25

⇒ x = √25

⇒ x = 5, -5; ignore -5

Now, the sum of the numbers, by putting value of x = 5

= 3x + 4x + 5x

= 12x

= 12(5)

= 60

Hence, The sum of the 3 numbers is 60