Question

Find the value of $x$ if the following are in continued proportion. $6,9,x$$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,

$a=6$

$b=9$

$c=x$

It is written as $6:9::9:x$

First and last term is called extreme terms, that is $6$ and $x$ and $9$ and $9$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 6\times x=9\times 9 \\ x=\frac{9\times 9}{6} \\ x=\frac{{\displaystyle \stackrel{3}{\cancel{9}}\times \stackrel{4.5}{\cancel{9}}}}{{\displaystyle \underset{\underset{1}{\cancel{2}}}{\cancel{6}}}} \\ x=3\times 4.5 \\ \therefore x=13.5 \end{gathered}$$

Hence the value of $x$is $13.5$