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# What is the mean proportional of 8 and 18?(a) 12(b) 144(c) 26(d) 13

Last updated date: 22nd Jul 2024
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Hint: Assume x as the mean proportional of 8 and 18. Now, write the expression in proportion form as 8: x:: x: 18 and use the basic theorem of a proportion given as ‘the product of means is equal to the product of extremes’. Consider the two x as the means and 8, 18 as the extremes. Solve for the value of x to get the answer.

\begin{align} & \Rightarrow x\times x=a\times b \\ & \Rightarrow {{x}^{2}}=ab \\ & \Rightarrow x=\sqrt{ab} \\ \end{align}
\begin{align} & \Rightarrow x=\sqrt{8\times 18} \\ & \Rightarrow x=\sqrt{144} \\ & \therefore x=12 \\ \end{align}
Note: You must remember the basic theorem of proportion to solve the above question. You may relate the obtained relation with that of the formula of geometric mean of two numbers so we can say that the mean proportional between two numbers is nothing but the geometric mean of the two numbers. The mean proportional relation can also be written as $\dfrac{a}{x}=\dfrac{x}{b}$.