Question

Find the mean proportionals that lie between each of the following pairs of numbers. 
1 and 1/25​

Answer 1

Given :-

The two numbers are 1 and 1/25

To find :-

The mean proportional.

Solution :-

Formula method :-

Given two numbers = 1 and 1/25

We know that

The mean proportional of a and b is √(ab)

The mean proportional of 1 and 1/25

= √[1×(1/25)]

=> √(1/25)

=> 1/5

Standard Method :-

Given two numbers = 1 and 1/25

Let the mean proportional of them be X

Then,

1 : X :: X : (1/25)

Since, They are in proportion then The product of means = The product of extremes

=> X×X = 1×(1/25)

=> X² = 1/25

=> X = √(1/25)

=> X = 1/5

Answer :-

The Mean Proportional of 1 and 1/25 is 1/5

Used formulae:-

→ The mean proportional of a and b is √(ab)

→ In proportion, The product of means

= The product of extremes

Answer 2

Step-by-step explanation:

Given :-

The two numbers are 1 and 1/25

To find :-

The mean proportional.

Solution :-

Formula method :-

Given two numbers = 1 and 1/25

We know that

The mean proportional of a and b is √(ab)

The mean proportional of 1 and 1/25

= √[1×(1/25)]

=> √(1/25)

=> 1/5

Standard Method :-

Given two numbers = 1 and 1/25

Let the mean proportional of them be X

Then,

1 : X :: X : (1/25)

Since, They are in proportion then The product of means = The product of extremes

=> X×X = 1×(1/25)

=> X² = 1/25

=> X = √(1/25)

=> X = 1/5

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