Question

Three numbers are in ration $2: 3: 4$. If sum of their squares is 1044 , then the sum of the numbers is___

Answer 1

Let the numbers be $2 x, 3 x$ and $4 x$ respectively. Then
According to question,
$ (2 x)^2+(3 x)^2+(4 x)^2=1044 $
$ \Rightarrow 4 x^2+9 x^2+16 x^2=1044$
$\Rightarrow 29 x^2=1044$
$ \Rightarrow x^2=\frac{1044}{29} $
$ \Rightarrow x^2=36 $
$ \Rightarrow x=\sqrt{36}$
$ \Rightarrow x=6$
$\therefore$ The number are
$ 2 x=2 \times 6=12, $
$3 x=3 \times 6=18, $
$4 x=4 \times 6=24$
$\therefore$ Sum of the number $=12+18+24=54$