Question

Find the mean proportional between $\text{9 and 144}$.

Answer 1

Explanation:

Let the mean proportional between $\text{9 and 144}$ is $\text{a}$, it means,

$\text{9:a::a:144}$ becomes in proportion.

We know that, $\text{Product of extremes terms = Product of means terms}$.

$$\begin{gathered} \Rightarrow a\times a=9\times 144 \\ \Rightarrow a^2=9\times 144 \\ \Rightarrow a=\sqrt{9\times 144} \\ \Rightarrow a=3\times 12 \\ \Rightarrow a=36 \end{gathered}$$

Hence, the mean proportional between $\text{9 and 144}$ is $36$.