Question

Find the fourth proportion in each of the following:

$21,27,14$

Answer 1

Given

$21,27,14$

It is written as $21:27::14\hspace{0.17em}:x$

First and last term is called extreme terms, that is $21$ and $x$ and $27$ and $14$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 21\times x=27\times 14 \\ x=\frac{27\times 14}{21} \end{gathered}$$

$x=\frac{{\displaystyle \stackrel{9}{\cancel{27}\times \stackrel{2}{\cancel{14}}}}}{{\displaystyle \underset{\underset{1}{\cancel{7}}}{\cancel{21}}}}$

$$\begin{gathered} x=9\times 2 \\ \therefore x=18 \end{gathered}$$

Hence the fourth proportion $21,27,14$ is $18.$