Question

Find the third proportional to $12$ and $30$.

Answer 1

Let the third proportional to $12$ and $30$ is $\text{a}$

So, $\text{12:30::30:a}$ becomes in proportion

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

$$\begin{gathered} \Rightarrow a\times 12=30\times 30 \\ \Rightarrow 12a=900 \\ \Rightarrow a=\frac{900}{12} \\ \Rightarrow a=75 \end{gathered}$$

Hence, the third proportional to $12$ and $30$ is $75$.