Question

Find the value of $x$ if the following are in continued proportion.

$14,21,x$

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,

$a=14$

$b=21$

$c=x$

It is written as $14:21::21:x$

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

product of extreme terms = product of middle terms

$$\begin{gathered} 14\times x=21\times 21 \\ x=\frac{21\times 21}{14} \\ x=\frac{{\displaystyle \stackrel{3}{\cancel{21}}\times \cancel{\stackrel{10.5}{21}}}}{{\displaystyle \underset{\underset{1}{\cancel{2}}}{\cancel{14}}}} \\ x=3\times 10.5 \\ \therefore x=31.5 \end{gathered}$$

Hence, the value of $x$is $31.5$