Question

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

Answer 1

The ratio of three numbers is

so , let the numbers be

So, According To The Question →

Note that the LCM =144.
$\to (36x^2+16x^2+9x^2)=244\ast 144$

$\to 61x^2=244\times 144$

$\to x^2=\frac{(244\times 144}{61}$
$\to x^2=\frac{244\times 144}{61}$
$\to {\sqrt{x}}^2=\sqrt{5}76$
or, x = 24

Therefore , the numbers are →

$\frac{1x}{2}=\frac{24}{2}=12$
$\frac{1x}{3}=\frac{24}{3}=8$

Answer → The numbers are 12 , 8 and 6.