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

Answer: 54

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