Question

Find three numbers in the ratio 1 : 2 : 3, so that the sum of their squares is equal to 504

(a) 6, 12,18

(b) 3,6, 9

(c) 4, 8, 12

(d) 5,10,15​

Answer 1

Answer:

a 6;12 ,18 is the right answer

all the best for your studies

Answer 2

Given that:

Ratio of three numbers=$\rm{1:2:3}$

The sum of there squares=$\rm{504}$

To find:

• The three numbers

Solution:

Let the three numbers be,

$\rm{1x ,2x ,3x}$

According to Question:

Squares of the numbers:

$\rm{(1x)²=1x²}$

$\rm{(2x)²=4x²}$

$\rm{(3x)²=9x²}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\rm⟾1x²+4x²+9x²=504$

$\rm⟾5x²+9x²=504$

$\rm⟾14x²=504$

$\rm⟾x²=\dfrac{504}{14}$

$\rm⟾x²=36$

$\rm⟾x=\sqrt{36}$

$\rm⟾x=\sqrt{6×6}$

$\rm⟾x=6$

Now ,

1. The first number=$\rm\red{1x=1×6=6}$
2. The second number=$\rm\blue{2x=2×6=12}$
3. The third number=$\rm\pink{3x=3×6=18}$

Therefore,the option (a) is correct.

Hope,its helpful!