Question

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

Answer 1

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.

Complete step by step answer:
Here we have been asked to find the mean proportional of 8 and 18. Let us see the process to calculate the mean proportional of two numbers.
Now, when we are provided with any two non – zero numbers say (a and b) and we have to find their mean proportional then we assume the mean proportional as x and write the general form of it given as a: x:: x: b. We know that the product of means is equal to the product of extremes in a proportion relation where a and b are extremes and the two x are means, so mathematically we have,
$\begin{align}
  & \Rightarrow x\times x=a\times b \\
 & \Rightarrow {{x}^{2}}=ab \\
 & \Rightarrow x=\sqrt{ab} \\
\end{align}$
Let us come to the question. Relating it with the above condition we can assume the mean proportional as x and we have a = 8 and b = 18, substituting these values in the above relation we get,
$\begin{align}
  & \Rightarrow x=\sqrt{8\times 18} \\
 & \Rightarrow x=\sqrt{144} \\
 & \therefore x=12 \\
\end{align}$

So, the correct answer is “Option a”.

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 $\dfrac{a}{x}=\dfrac{x}{b}$.