Question

If the first and third numbers of four positive number is continued proportion be 3 and 12 respectively
then fourth number is ​

Answer 1

Required third number is 12.

Step-by-step explanation:

Let,

First number be a

Third number be 4a / 9, since third number is 4 / 9 of the first number.

From the properties of ratio and proportion : If a, b and c are in continued proportion, then

= > a / b = b / c

= > a x c = b x b

= > ac = b^2 , where b is the middle term & a and c are the remaining terms.

Here,

Middle terms is 18 , and the remaining terms are a and 4a / 9.

On the basis of the identity given above :

= > 18^2 = a x ( 4a / 9 )

= > 18^2 = a x a x 4 / 9

= > 18^2 = a^2 x ( 2 / 3 )^2

= > 18^2 ( 2a / 3 )^2

= > 18 = 2a / 3

= > 18 x 3 / 2 = a

= > 27 = a

Hence,

= > Third number is : 4 / 9 x 27

= > Third number is : 4 x 3

= > Third number is : 12

Hence the required third number is 12.