Three positive numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 2349, then the numbers respectively are:

Correct option is B

Given:

The ratio of three numbers is 2 : 3 : 4.

The sum of their squares is 2349.

Solution:

Let the three numbers be 2x, 3x, 4x

Now,

​$$(2x)^2 + (3x)^2 + (4x)^2 = 2349$$​​

​$$4x^2 + 9x^2 + 16x^2 = 2349$$​​

​$$x^2 = \frac{2349}{29} = 81$$​​

x = $$\sqrt{81} = 9$$​​

The three numbers are:

2x = 2 × 9 = 18

3x = 3 × 9 = 27

4x = 4 × 9 = 36