Question

Question #68e8a

Answer 1

`10√2,15√2,20√2`

Explanation:

Let the numbers be 2x,3x,4x
According to the question
`(2x)^2 + (3x)^2 + (4x)^2 = 1450`
`4x^2 + 9x^2 + 16x^2 = 1450`
`29x^2 = 1450`
`x^2 = 50`
`x = 5√2 or √50`

So,2x = 10√2
3x = 15√2
4x = 20√2

Answer 2

`{10sqrt(2), 15sqrt(2),20sqrt(2)}` or `{-10sqrt(2),-15sqrt(2),-20sqrt(2)}`

Explanation:

If the 3 numbers are in the ratio `2:3:4`
then there is some constant `color(blue)k` such that the numbers are `2color(blue)k, 3color(blue)k, and 4color(blue)k`

The sum of the squares of these 3 numbers will be
`(2color(blue)k)^2+(3color(blue)(k))^2+(4color(blue)k)^2=1450`

`4color(blue)k^2+9color(blue)k^2+16color(blue)k^2=1450`

`29color(blue)k^2=1450`

`color(blue)k^2=50`

`color(blue)k=+-5sqrt(2)`

and the 3 numbers are
`{10sqrt(2), 15sqrt(2),20sqrt(2)}` or `{-10sqrt(2),-15sqrt(2),-20sqrt(2)}`