Question

The mean proportional between 234 and 104 is
$
  {\text{a}}{\text{. 12}} \\
  {\text{b}}{\text{. 39}} \\
  {\text{c}}{\text{. 54}} \\
  {\text{d}}{\text{. None of these}} \\
$

Answer 1

Hint – The mean proportional between the two numbers (a, b) is given as $a:x::x:b$, where x is the mean proportional, use this concept to reach the solution of the problem.
Given number is 234 and 104
Let the mean proportion of these numbers be x.
Then according to mean proportional property convert then in equation which is given as
$234:x::x:104$
$ \Rightarrow \dfrac{{234}}{x} = \dfrac{x}{{104}}$
$
   \Rightarrow {x^2} = 104 \times 234 \\
   \Rightarrow {x^2} = 24336 \\
   \Rightarrow x = \sqrt {24336} = \sqrt {{{\left( {156} \right)}^2}} = 156 \\
$
So, the mean proportion of 234 and 104 is 156.
So, this is the required answer.
Hence option (d) is correct.

Note – In such types of questions the mean proportional of two given numbers is also calculated by taking the square root of the given numbers, so directly take the square root of the numbers and simplify, we will get the required answer.