Question

Find the mean proportional for each of the following:

(iv) $0.25,40000$

Answer 1

Calculate the mean proportional:

Let $x$ be the mean proportional.

If $x$ is the mean proportional between $a$ and $b$, then $a:x::x:b$.

Then for the numbers $0.25,40000$, the equivalent proportional expression is $0.25:x::x:40000$.

$$\begin{gathered} \Rightarrow 0.25:x=x:40000(Changingtheproportionalitysigntoequalsign) \\ \Rightarrow \frac{{\displaystyle 0.25}}{x}=\frac{x}{{\displaystyle 40000}} \\ \Rightarrow x·x=0.25·40000(Crossmultiplyingbothsides) \\ \Rightarrow x^2=10000 \\ \therefore x=\pm 100(Takingsquarerootonbothsides) \end{gathered}$$

As $-100$ does not lie between the given two numbers, therefore, the mean proportional is 100.

Final Answer: The mean proportional is 100.