Question

The sum of squares of three numbers who are in a ratio of 2:3:4 is 725. find out the numbers

Answer 1

Let first number be 2x
Second number be 3x
And third number be 4x

${(2x)}^{2} + {(3x)}^{2} + {(4x)}^{2} = 725 \\ \\ 4 {x}^{2} + 9 {x}^{2} + 16 {x}^{2} = 725 \\ \\ 29 {x}^{2} = 725 \\ \\ {x}^{2} = \frac{725}{29} \\ \\ {x}^{2} = 25 \\ \\ x = \sqrt{25} \\ \\ x = 5$

First number = 2x = 2 X 5 = 10
Second number = 3x = 3 X 5 = 15
Third number = 4x = 4 X 5 = 20


Check
$LHS = {(2x)}^{2} + {(3x)}^{2} + {(4x)}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = {(10)}^{2} + {(15)}^{2} + {(20)}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = 100 + 225 + 400 \\ \\ \: \: \: \: \: \: \: \: \: \: = 725 = RHS$

Answer 2

Answer:

numbers are 2k, 3k, and 4k for some positive constant k.

The sum of their squares is equal to







Divide both sides by 29





Get the positive square root of both sides.

k = 5

So 2k = 10, 3k = 15, and 4k = 20.

The numbers are , , and