# Third Proportional

To find third proportional of any two numbers let say a and b be two numbers and c is in third proportion with a and b

Then,

a : b = b : c

Third Proportional Example 1

Find the third proportion to 6 and 12?

Explanation:

To find third proportional of any two numbers let say a and b be two numbers and c is in third proportion with a and b

Then,

a : b = b : c

Let, the third proportion to 6 and 12 be a

6 : 12 :: 12 : a

(Product of Extremes= Product of Means)

Here, Extremes are= 6 and a

Means are = 12 and 12

6 x a = 12 x 12

a = (12 x 12)/6 = 24

Hence, the value of ‘a’ is 24

Third Proportional Example 2

Find the third proportion to 8 and 16?

Explanation:

To find third proportional of any two numbers let say a and b be two numbers and c is in third proportion with a and b

Then,

a : b = b : c

Let, the third proportion to 8 and 16 be a

8 : 16 :: 16 : a

(Product of Extremes= Product of Means)

Here, Extremes are= 8 and a

Means are = 16 and 16

8 x a = 16 x 16

a = (16 x 16)/8 = 32

Hence, the value of ‘a’ is 32

Third Proportional Example 3

Find the third proportion to 16 and 24?

Explanation:

To find third proportional of any two numbers let say a and b be two numbers and c is in third proportion with a and b

Then,

a : b = b : c

Let, the third proportion to 16 and 24 be a

16 : 24 :: 24 : a

(Product of Extremes= Product of Means)

Here, Extremes are= 16 and a

Means are = 24 and 24

16 x a = 24 x 24

a = (24 x 24)/16  = 36

Hence, the value of ‘a’ is 36

Third Proportional Example 4

Find the third proportion to 5 and 25?

Explanation:

To find third proportional of any two numbers let say a and b be two numbers and c is in third proportion with a and b

Then,

a : b = b : c

Let, the third proportion to 5 and 25 be a

5 : 25 :: 25 : a

(Product of Extremes= Product of Means)

Here, Extremes are= 5 and a

Means are = 25 and 25

5 x a = 25 x 25

a = (25 x 25)/5 = 125

Hence, the value of ‘a’ is 125

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