Question

find three positive numbers in the ratio 2:3:5, the sum of whose squares is 950

Answer 1

let the three numbers be 2A, 3A and 5A,


then

according to the question, we have

(2A)²+(3A)²+(5A)²=950,

4A²+9A²+25A²=950,

38A²=950,

then

A²=950/38,

A²=2,

then

A=5,


therefore

1st number=2×5=10,

2nd number=3×5=15,

3rd number=5×5=25

Answer 2

Let the numbers be 2x , 3x and 5x

Therefore

4x² + 9x² + 25x² = 950

38x² = 950

x² = 950/38

x² = 25

x = 5

The numbers will be

1st number = 2x = 10

2nd number = 3x = 15

3rd number = 5x = 25