Question

three natural numbers are in the ratio 2:3:4 if the sum of squares of these numbers is 116 then determine the numbers

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Answer 1

let numbers be 2x , 3x , 4x . .

a/q.

4x^2 + 9x^2 + 16x^2 = 116.

29x^2 = 116

x^2 = 4.

therefore x=2.

so the numbers are 4,6,8...

thats the ans..

if u like mark it a brainlist ans.

Answer 2

Answer:

Required all numbers are 4,6 and 8.

Step-by-step explanation:

Given,three natural numbers are in the ratio 2:3:4.

Let first number be 2x and second number be 3x and third number be 4x.

Now square of 2x $= {(2x)}^{2} = 4 {x}^{2}$

and square of 3x $= {(3x)}^{2} = 9 {x}^{2}$

and square of 4x $= {(4x)}^{2} = 16 {x}^{2}$

Now,

sum of squares of all numbers

$= 4 {x}^{2} + 9 {x}^{2} + 16 {x}^{2} \\ = (4 + 9 + 16) {x}^{2} \\ = 29 {x}^{2}$

It is given that the sum of squares of these numbers is 116.

According to question,

$29 {x}^{2} = 116 \\ {x}^{2} = \frac{116}{29} \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ x = 2$

So, first number $= 2 \times 2 = 2$

and second number $= 3 \times 2 = 6$

and third number $= 4 \times 2 = 8$

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