Question

Three positive numbers are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ . Find the number if the sum of their square is 244 .

Answer 1

Given $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

Let no. $\frac{x}{2},\frac{x}{3},\frac{x}{4}$

${\left(\frac{x}{2}\right)}^2+{\left(\frac{x}{3}\right)}^2+{\left(\frac{x}{4}\right)}^2=244$

$x^2[\frac{1}{4}+\frac{1}{5}+\frac{1}{16}]=244$

$x^2\left[\frac{36+16+9}{9\times 16}\right]=244$

$x^2=\frac{244\times 9\times 16}{61}=4\times 9\times 16$

$x=\sqrt{576}$

$x=24$

So. numbers = $\frac{24}{2},\frac{24}{3},\frac{24}{4}$

$=12,8,6$