Question

Find the third proportional to .

$8$ and $12$

Answer 1

Let the three quantities are $a,b,c$

In three quantities $a,b,c$ are written as $=a:b::b:c$

Let. third proportional $\left(c\right)=x$

So,

$$$$\begin{gathered} a=8 \\ b=12 \\ c=x \end{gathered}$$

It is written as $8:12::12:x$

First and last term is called extreme terms, that is $8$ and $x$ and $12$ and $12$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 8\times x=12\times 12 \\ x=144 \\ x=\frac{{\displaystyle \stackrel{18}{\cancel{144}}}}{\cancel{8}} \\ \therefore x=18 \end{gathered}$$

Hence the third proportional to $8$ and $12$ is $18.$