Question

Find the mean proportional for each of the following:

(v)$₹5,₹125$

Answer 1

Find 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 $5,125$, the equivalent proportional expression is $5:x::x:125$.

$$\begin{gathered} \Rightarrow 5:x=x:125(Changingtheproportionalitysigntoequalsign) \\ \Rightarrow \frac{{\displaystyle 5}}{x}=\frac{x}{{\displaystyle 125}} \\ \Rightarrow x·x=5·125(Crossmultiplyingbothsides) \\ \Rightarrow x^2=625 \\ \therefore x=\pm 25(Takingsquarerootonbothsides) \end{gathered}$$

As $-25$ does not lie between the given two numbers, therefore, the mean proportional is $₹25$.

Final Answer: The mean proportional is $₹25$.