Question

The mean proportional between two numbers is $28$ and their third proportional is $224$. Find the two numbers.

Answer 1

Let the numbers be a and b

$c=224$

$\sqrt{ab}=28$

$ab={28}^2$

$ab=784$

$a=\frac{784}{b}$

We know that ,$ac=b^2$

$c=\frac{b^2}{a}$

Substitute $a=\frac{784}{b}$

$224=\frac{b^2}{\frac{784}{b}}$

$224=\frac{b^3}{784}$

$b^3=224\times 784$

$b=56$

$a\times 56=784$

$a=\frac{784}{56}$

$a=14$

The numbers are 56 and 14