Question

if the geometric mean of A and B is 6 and the geometric mean of B and C is 12 then find the ratio of C & A​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

The geometric mean of A and B is $= \pm \: \sqrt{AB}$

TO DETERMINE

The geometric mean of A and B is 6 and the geometric mean of B and C is 12 then find the ratio of C & A

CALCULATION

Now The geometric mean of A and B is$= \pm \: \sqrt{AB}$

Again The geometric mean of B and C is$= \pm \: \sqrt{BC}$

So by the given condition

$\pm \: \sqrt{AB} = 6$

$\implies \: AB = 36$

And

$\pm \: \sqrt{BC} \: = 12$

$\implies \: BC \: = 144$

So

$\displaystyle \: \frac{BC}{AB} = \frac{144}{36}$

$\implies \: \displaystyle \: \frac{C}{A} = \frac{4}{1}$

$\therefore \: \displaystyle \: C \: : A = 4 \: : \: 1$