Question

Find the third proportional to:

$5,10$

Answer 1

Let the third proportional be $x$, Then-

so the proportion be, $5:10::10:x$

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

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

so, now in $5:10::10:x$

$a=5,b=10,c=10,d=x$

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

$$\begin{gathered} \Rightarrow 5\times x=10\times 10 \\ \Rightarrow 5x=100 \\ \Rightarrow x=\frac{100}{5} \\ \Rightarrow x=20 \end{gathered}$$

Hence, the third proportion be $20$