Question

Find the mean proportional between $\text{9}$ and $25$.

Answer 1

Let the mean proportional between $\text{9}$ and $25$ is $\text{a}$, it means,

$\text{9:a::a:25}$ becomes in proportion

Therefore, $\text{Product of extremes terms = Product of means terms}$

$$\begin{gathered} \Rightarrow a\times a=9\times 25 \\ \Rightarrow a^2=9\times 25 \\ \Rightarrow a=\sqrt{9\times 25} \\ \Rightarrow a=3\times 5 \\ \Rightarrow a=15 \end{gathered}$$

Hence, the mean proportional between $\text{9}$ and $25$ is $15$.