Question

Find the fourth proportional to:

$2.1,1.5,8.4$

Answer 1

Let the fourth proportional be $x$, Then-

so the proportion be, $2.1:1.5::8.4:x$

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

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

so, now in $2.1:1.5::8.4:x$

$a=2.1,b=1.5,c=8.4,d=x$

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

$$\begin{gathered} \Rightarrow 2.1\times x=1.5\times 8.4 \\ \Rightarrow 2.1x=12.6 \\ \Rightarrow x=\frac{12.6}{2.1} \\ \Rightarrow x=6 \end{gathered}$$

Hence, the fourth proportion be $6$