FINDING MEAN PROPORTION -
If you are given a and c and need to find b, the mean proportional:-
a b
-------- = --------
b c
Or, a x c = b²
Or, b = √(a x c)
The mean proportion (or geometric mean) between two numbers a and b is a value x such that the ratio of aaa to x is the same as the ratio of x to b. In mathematical terms, x is the mean proportional between a and b if:-
a x
-------- = --------
x b
Formula to Find the Mean Proportional:-
To find the mean proportional x between two numbers a and b, you can use the following formula:-
a x b = x²
Or, x = √(a x b)
Example.1) Find the mean proportion between 9 & 16
Ans.)
Step 1:- Identify the numbers a and b.
As per the given condition a = 9, b = 16, need to find out value of 'x'.
Step 2:- Apply the formula:
x = √(a x b) = √(9 x 25) = √225
Step 3:- Calculate the square root:
√225 = √15² = 15
So, the mean proportional between 9 and 25 is 15. (Ans.)
Example.2) Find the mean proportional between 4 and 25.
Step 1:- Identify the numbers a and b.
Step 2:- Apply the formula:
x = √(a x b) = √(4 x 25) = √100
Step 3:- Calculate the square root:
√100 = √10² = 10
So, the mean proportional between 4 and 25 is 10. (Ans.)
Example.3) Find the mean proportional between 9 and 16.
Ans.)
Step 1: Identify the numbers a and b.
Step 2: Apply the formula:
x = √(a x b) = √(9 x 16) = √144
Step 3: Calculate the square root:
√144 = √12² = 12
So, the mean proportional between 9 and 16 is 12. (Ans.)
The mean proportional is often used in geometry, particularly in similar triangles, where the lengths of corresponding sides are in proportion. It also appears in problems involving right triangles and the relationships between the segments of the hypotenuse.
The mean proportional between two numbers a and b is found using the formula √(a × b). This value represents the geometric mean and is useful in various mathematical contexts, especially in problems involving ratios, proportions, and geometry.