**What is Mean Proportion?**

If a and b be two numbers and c is mean proportional between a and b

Then,

a : c = c : b

**Mean Proportion Example 1**

Find the mean proportional between 25 and 100 ?

**Explanation:**

Let, the mean proportional between 25 and 100 be ‘ a ‘

25 : a :: a : 100

(Product of extremes = Product of means)

Here, Extremes are 25 and 100

Means are a and a

25 x 100 = a x a

a² = 25 x 100 = 2500

a = 50

Hence, the value of ‘a’ is 50

**Mean Proportion Example 2**

Find the mean proportional between 10 and 40 ?

**Explanation:**

Let, the mean proportional between 10 and 40 be ‘ a ‘

10 : a :: a : 40

(Product of extremes = Product of means)

Here, Extremes are 10 and 40

Means are a and a

10 x 40 = a x a

a² = 10 x 40 = 400

a = 20

Hence, the value of ‘a’ is 20

**Mean Proportion Example 3**

Find the mean proportional between 64 and 16 ?

**Explanation:**

Let, the mean proportional between 64 and 16 be ‘ a ‘

64 : a :: a : 16

(Product of extremes = Product of means)

Here, Extremes are 64 and 16

Means are a and a

64 x 16 = a x a

a² = 64 x 16 = 1024

a = 32

Hence, the value of ‘a’ is 32

**Mean Proportion Example 4**

Find the mean proportional between 9 and 4 ?

**Explanation:**

Let, the mean proportional between 9 and 4 be ‘ a ‘

9 : a :: a : 4

(Product of extremes = Product of means)

Here, Extremes are 9 and 4

Means are a and a

9 x 4 = a x a

a² = 9 x 4 = 36

a = 6

Hence, the value of ‘a’ is 6

**Click here for Ratio and Proportion Problems and Solutions for Class 7**