Question

Mark the correct alternative in the following question:

The mean proportional of 6 and 24 is

(a) 15 (b) 12 (c) 8 (d) 144

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{the}\mathrm{mean}\mathrm{proportional}\mathrm{of}6\mathrm{and}24.\mathrm{Then}, \\ \frac{6}{\mathrm{x}}=\frac{x}{24} \\ \Rightarrow x^2=6\times 24\left(\mathrm{By}\mathrm{cross}\mathrm{multiplication}\right) \\ \Rightarrow x^2=144 \\ \Rightarrow x=\sqrt{144} \\ \therefore x=12 \end{gathered}$$

So, the mean proportional of 6 and 24 is 12.

Hence, the correct alternative is option (b).