Question

Find the mean proportional between 4 and 9.

Answer 1

Hint: The term means proportion is also referred to as the geometric mean. The term means when used alone or in context with mean, median or mode refer to the arithmetic means of finding an average. Geometric means deals with multiplication. The mean proportion between two numbers of a ratio is calculated by taking the square root of multiplication of the two numbers.
As we know that mean proportion is given by
$\therefore mean\,proportion = \sqrt {pq} $
So we use this formula and put values in the formula and get the mean proportion for a given term.

Complete answer:
As given in the question,
First term, $p = 4$
Second term, $q = 9$
As we know that mean proportion is
 $\therefore mean\,proportion = \sqrt {pq} $
Put the values in the giving formula,
$ \Rightarrow mean\,proportion = \sqrt {4 \times 9} $
solving further,
$ \Rightarrow mean\,proportion = \sqrt {36} $
Solve square root for given term,
$ \Rightarrow mean\,proportion = \sqrt {6 \times 6} $
$ \Rightarrow mean\,proportion = 6$
The mean proportional between 4 and 9 is $6$

Note:
In geometric mean or mean proportion, the values of both ‘X’ are equal. Mean proportion is also known as Geometric mean. There is a right angle mean proportion theorem which has two theorems. The altitude that is drawn to the hypotenuse of a right angle triangle creates two triangles that are similar to the original triangle and each other. The leg rule states that the mean proportion of the hypotenuse and the portion of the leg.