Question

please let me know the answer
the question is
The sum of squares of three numbers which are in the ratio 2:3:4 is 725 . what are the numbers

Answer 1

Let the three numbers are in the ratio be 2x: 3x: 4x.


Given that sum of squares (2x)^2 + (3x)^2 + (4x)^2 = 725

                                             29x^2 = 725

                                                 x^2 = 25

                                                    x = 5.

Then 2x = 10, 3x = 15,4x = 20.

The three numbers are 10,15,20.

Answer 2

Let the common ratio be 'k'. The numbers are 2k, 3k, 4k. According to the given condition, (2k)²+(3k)²+(4k)² = 725 ⇒ 4k²+9k²+16k² = 725 ⇒ 29k²=725.
k² = 25 ⇒ k = +5 or -5. The numbers are 10, 15, 20 or -10, -15, -20.