Question

Find the fourth proportional to:

$8,14,16$

Answer 1

Let the fourth proportional be $x$, Then-

so the proportion be, $8:14::16:x$

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

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

so, now in $8:14::16:x$

$a=8,b=14,c=16,d=x$

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

$$\begin{gathered} \Rightarrow 8\times x=14\times 16 \\ \Rightarrow 8x=224 \\ \Rightarrow x=\frac{224}{8} \\ \Rightarrow x=28 \end{gathered}$$

Hence, the fourth proportion be $28$