Question

Find the mean proportion between $3$ and $12.$

Answer 1

Let the mean proportion between $3$ and $12$ be $=x$

it is written as $3:x::x:12$

First and last term is called extreme terms, that is $3$ and $12$ and $x$ and $x$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 3\times 12=x\times x \\ {x}^2=36 \\ x=\sqrt{36} \\ \therefore x=6 \end{gathered}$$

Hence the mean proportion between $3$ and $12$ is $6.$