Question

Find the mean proportional between:

$9and25$

Answer 1

Let the mean proportional be $x$, then-

$9:x::x:25$

Now, if $a:b::c:d$are in proportion.

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

So, here we have $9:x::x:25$

$a=9,b=x,c=x,d=25$

by using $eq\left(1\right)$ we have

$$\begin{gathered} \Rightarrow 9\times 25=x\times x \\ \Rightarrow x^2=225 \\ \Rightarrow x=\sqrt{225} \\ \Rightarrow x=15 \end{gathered}$$

Hence the mean proportional between $9and25$ is $15$