Question

Three numbers are in the ratio 2 : 3 : 5. If the sum of their squares is 15200 , find the numbers .

Answer 1

Let the numbers be $2x$, $3x$, and $5x$.

Sum of squares = $15200$

ATQ,

$(2x)^2 + (3x)^2 + (5x)^2 = 15200$

=> $4x^2 + 9x^2 + 25x^2 = 15200$

=> $38x^2 = 15200$

=> $x^2 = 400$

=> $x = \pm \sqrt{400}$

=> $x = \pm 20$

Since those are numbers and not integers, so rejecting $x = - 20$,

we get,

$x = + 20$.

Therefore, the numbers are $40$, $60$, $100$.