Question

Find the mean proportional between $25and36.$

Answer 1

Find the mean proportional:

Let, $x$ be the mean proportional between $25and36.$

Now, $25$, $x$ and $36$ are in continued proportion.

So, $25:x::x:36$

$\Rightarrow \frac{25}{x}=\frac{x}{36}$

$\Rightarrow x^2=25\times 36$

$\Rightarrow x=\sqrt{900}$

$\Rightarrow x=30$

Hence, the mean proportional between $25and36$ is $30$.