Question

three numbers are in the ratio 1:2:3 and the sum of their squares is 504 the largest of the numbers is​

Answer 1

Answer:

18

Step-by-step explanation:

Let the numbers be x, 2x and 3x respectively.

According to question,

$x^{2}$ + $(2x)^{2}$ + $(3x)^{2}$   =   504

$x^{2}$ + $4x^{2}$ + $9x^{2}$        =   504

                $14x^{2}$      =   504

                     $x^{2}$    =    504 / 14

                    $x^{2}$     =     36

                     x     =    $\sqrt{36}$

                      x    =    6

The greatest number be 3x  =   3 * 6  = 18

Answer 2

Question:

Three numbers are in the ratio of 1:2:3 and the sum of their square is 504 the largest of the number is ?

Answers :

Given :

Ratio is 1:2:3

Sum of the squares = 504

Required to Find :

Largest Number

Solution:

Given ratio = 1:2:3

So,

Let the numbers be 1x , 2x , 3x

In the question they gave us an hint

that is sum of the squares is 504.

so , using this we can find our solution

here,

Let the numbers be 1x , 2x , 3x

Now square each and every number

$(1x {)}^{2} \: \: (2x {)}^{2} \: \: (3x {)}^{2} \\ 1 {x}^{2} \: \: 4 {x}^{2} \: \: 9 {x}^{2}$

So, Now the number are

1x^2 ,4x^2 , 9x^2

Now , add the three numbers we get

$1 {x}^{2} + 4 {x}^{2} + 9 {x}^{2} = 14 {x}^{2}$

Here,

equal this with the sum of the squares of the numbers

That is 504.

$14 {x}^{2} = 504 \\ {x}^{2} = \frac{504}{14} \\ {x}^{2} = 36 \\ x = \sqrt{36} \\ x = 6$

Therefore,

The value of x is 6

so,

The numbers are

1. First number =1 (x) = 1 (6) = 6
2. second number = 2 (x) = 2 (6) = 12
3. Third number = 3 (x) = 3 (6) = 18

Therefore,

The largest number is 18 .

verification:

Numbers are 6 , 12 , 18

squaring the numbers

(6)^2 , (12)^2 , (18)^2

= 36 , 144 , 324

Now these numbers above they should be equal to 504

so,

36 + 144 + 324 = 504

504 = 504

504 = 504

hence verified