Question

Find the mean proportion between $16$ and $36$.

Answer 1

Finding the mean proportion between $16$ and $36$:

If three quantities $a$, $b$ and $c$ are in continued proportion, that is, if $a:b::b:c$, then $b^2=ac$.

This is as same as when four quantities are in proportion, then the product of extremes is equal to the product of means. When it is continued proportion, the product of means is basically the square of the mean/middle proportion as the second and the third term is the same.

Let the mean proportion between $16$ and $36$ be $x$.

So, $16:x::x:36$.

$\Rightarrow$$x^2=16\times 36$

$\Rightarrow$$x^2=576$

$\Rightarrow$$x=24$

Hence, the mean proportion between $16$ and $36$ is $24$.