Question

Find the mean proportion between:
(i) $3$ and $27$

Answer 1

Step: Calculating the required mean proportion
Let the required mean proportion be $x$.
$\therefore 3,x$ and $27$ are in continued proportion
$\Rightarrow 3:x=x:27$
$\Rightarrow x\times x=27\times 3$
(∵ Product of means = Product of extremes)
$\Rightarrow x^2=9\times 3\times 3$
$\Rightarrow x^2=9\times 9$
$\therefore x=9$
Hence, the required mean proportion is $9$.