Question

Find the mean proportion of 10 and 20

Answer 1

Step-by-step explanation:

Given:-

Given numbers are 10 and 20

To find:-

Find the mean proportion of 10 and 20

Solution:-

Given numbers = 10 and 20

Let the mean proportion of 10 and 20 be X

Then the proportion = 10:X::X:20

Product of extremes = 10×20=200

Product of means = X×X =X^2

In proportion, Product of means = Product of extremes

=>X^2=200

=>X=√200

=>X=√(2×100)

=>X=10√2

The mean proportion of 10 and 20 = 10√2

(or)

We know that

the mean proportion of the two numbers'a' and 'b' is √(ab)

We have

the two numbers 10 and 20

a= 10

b=20

Mean proportion = √(10×20)

=>√200

=>√(2×100)

=>10√2

The mean proportion of 10 and 20 = 10√2

Answer:-

The mean proportion of 10 and 20 = 10√2

Used formulae:-

• the mean proportion of the two numbers'a' and 'b' is √(ab)
• In proportion, Product of means = Product of extremes