Question

Find the mean proportional between:

$15and60$

Answer 1

Let the mean proportional be $x$, then-

$15:x::x:60$

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

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

So, here we have $15:x::x:60$

$a=15,b=x,c=x,d=60$

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

$$\begin{gathered} \Rightarrow 15\times 60=x\times x \\ \Rightarrow x^2=900 \\ \Rightarrow x=\sqrt{900} \\ \Rightarrow x=30 \end{gathered}$$

Hence the mean proportional between $15and60$ is $30$