Question

Find the fourth proportion in each of the following:

$16,48,27$

Answer 1

Given

$16,48,27$

It is written as $16:48::27\hspace{0.17em}:x$

First and last term is called extreme terms, that is $16$ and $x$ and $48$ and $27$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 16\times x=48\times 27 \\ x=\frac{48\times 27}{16} \end{gathered}$$

$x=\frac{{\displaystyle \stackrel{\stackrel{3}{\cancel{6}}}{\cancel{48}}}\times {\displaystyle 27}}{{\displaystyle \underset{\underset{1}{\cancel{2}}}{\cancel{16}}}}$

$$\begin{gathered} x=3\times 27 \\ \therefore x=81 \end{gathered}$$

Hence the fourth proportion $16,48,27$ is $81.$