Question

Find the fourth proportion in each of the following:

$54,76,108$

Answer 1

Given

$54,76,108$

It is written as $54:76::108\hspace{0.17em}:x$

First and last term is called extreme terms, that is $54$ and $x$ and $76$and $108$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 54\times x=76\times 108 \\ x=\frac{76\times 108}{54} \end{gathered}$$

$x=\frac{{\displaystyle \stackrel{4}{\cancel{76}}}\times {\displaystyle \stackrel{36}{\cancel{108}}}}{{\displaystyle \underset{\underset{1}{\cancel{3}}}{\cancel{54}}}}$

$$\begin{gathered} x=4\times 36 \\ \therefore x=144 \end{gathered}$$

Hence, the fourth proportion $54,76,108$ is $144.$