Question

Find the mean proportional between:

$0.9and2.5$

Answer 1

Let the mean proportional be $x$, then-

$0.9:x::x:2.5$

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

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

So, here we have $0.9:x::x:2.5$

$a=0.9,b=x,c=x,d=2.5$

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

$$\begin{gathered} \Rightarrow 0.9\times 2.5=x\times x \\ \Rightarrow x^2=2.25 \\ \Rightarrow x=\sqrt{2.25} \\ \Rightarrow x=1.5 \end{gathered}$$

Hence the mean proportional between $0.9and2.5$ is $1.5$