Introduction To Mean Proportional Between Two Numbers
The mean proportion of two positive numbers a and b is also a positive number x such that a/x = x/ b
. When solving,
X= 'sqrt(ab)'
When three quantities/numbers are given such that the ratio of the first and the second are equal to the ratio of the second and the third term, then the three terms are said to be in continued proportion. The second term is known as the mean proportion between the first and the third. The third term is called the third proportion. Mean proportion is also known as geometric mean
Finding Mean Proportional between Two Numbers
Steps to find mean proportional between two numbers:
Step 1 : Write the given two numbers in ratio form using mean value
Step 2 : Set the extreme /mean to a variable say x
Step 3 : Put x in the bottom of first number a and to the top of second number b
Step 4 : Equate the first ratio to second ratio such that 'a/x' = 'x/b'
Step 5 : Find the x value by taking the square root of the product of given 2 numbers a, b
Example Problems of Mean Proportional between Two Numbers
Ex 1:
Find the mean proportional between two numbers 24, 60?
Sol :
Let mean proportion be m
24/ m = m/ 60
m 2 = 24 * 60
m 2 = 1440
m = $sqrt{1440}$
m= 26. 83
Hence Mean proportional between 24 and 60 is 26. 83
Ex 2:
Find the mean proportional between two numbers 8 and 200
Sol:
m = ab
[Mean proportional between a and b.]
m = 'sqrt(8 * 200)'
[Replace a = 8 and b = 200.]
m = 'sqrt(8.8.5.5)' [Factor.]
m = 8 5 = 40
So, the mean proportional between two numbers 8 and 200 is 40.
Ex 3:
Find the mean proportional between the numbers 3, 6, 12