Question

Find two numbers such that the mean proportional between them $28$ and third proportionl to them is $224$.

Answer 1

Let the numbers are $a$ and $c$ then

As per the given condition-

$a:b=b:c\Rightarrow b^2=ac=784\Rightarrow a=\frac{784}{c}$ [Given that $b=28$]
$a:c=c:224$

$\Rightarrow c^2$ $=224a$

$\Rightarrow c^2=224\times \frac{784}{c}$
$\Rightarrow c^3=224\times 784\Rightarrow c=56$

So, $a=14$
Hence, the numbers are $14$ and $56$.