Question

If $3,x,12$are in continued proportion, find the value of $x$.

Answer 1

If $3,x,12$ are in continued proportion.

Then the proportion be, $3:x::x:12$

Now, if $a:b::c:d$be in proportion then

$a\times d=b\times c$ --------------------------------$eq\left(1\right)$

so, now in $3:x::x:12$

$a=3,b=x,c=x,d=12$

So, by $eq\left(1\right)$ we have,

$$\begin{gathered} \Rightarrow 3\times 12=x\times x \\ \Rightarrow x^2=36 \\ \Rightarrow x=\sqrt{36} \\ \Rightarrow x=6 \end{gathered}$$

Hence, the value of $x$ be $6$