Question

The sum of the squares of three numbers which are in the ratio $2:3:4$ is $725.$ What are these numbers?

• A. $10,15,20$
• B. $14,21,28$
• C. $20,15,30$
• D. $20,30,40$

Answer 1

The correct option is A $10,15,20$

Let the three numbers be 2x, 3x and 4x.
Given, $(2x{)}^2+(3x{)}^2+(4x{)}^2=725$
$\Rightarrow 4x^2+9x^2+16x^2=725\Rightarrow 29x^2=725$
$\Rightarrow x^2=25\Rightarrow x=5$
$\therefore$ The numbers are 10, 15 and 20.