Question

Find the fourth proportional in $\frac{1}{3},\frac{2}{5},6$.

Answer 1

Explanation:

Let the fourth proportional be $\text{x}$.

Then, the numbers becomes in proportion.

$\text{⇒}\frac{1}{3}\text{:}\frac{2}{5}\text{::6:x}$

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

$$\begin{gathered} \text{⇒x×}\frac{1}{3}\mathrm{=}\frac{2}{5}\times 6 \\ \mathrm{\Rightarrow }\frac{\mathrm{x}}{3}\mathrm{=}\frac{12}{5} \\ \Rightarrow \mathrm{x}=\frac{12}{5}\times 3 \\ \Rightarrow \mathrm{x}=\frac{36}{5} \end{gathered}$$

Hence, the fourth proportional is $\frac{36}{5}$.