Question

If 256 is the third proportional of a and b, where a:b=3:16 then find the value of a+b

Answer 1

Answer:

57

Step-by-step explanation:

Given,

a : b = 3 : 16

256 is the third proportional of a and b.

It means : a / b = b / 256

= > 3 / 16 = b / 256

= > ( 3 x 256 ) / 16 = b

= > 3 x 16 = b

= > 48 = b

Therefore,

= > a / b = 3 / 16

= > a / 48 = 3 / 16

= > a = ( 3 x 48 ) / 16

= > a = 3 x 3

= > a = 9

Hence,

= > a + b

= > 9 + 48

= > 57

Answer 2

Answer:

57

Step-by-step explanation:

a : b = 3 : 16

which means....

a = 3k & b = 16k

now....since third proportion c = 256

a : b : c = 3k : 16k : 256

therefore...since b^2 = a × c

(16k) ^2 = (3k) (256)

256 k^2 = 3 × 256 × k

k = 3

hence....

a = 3k = 3(3) = 9

b = 16k = 16(3) = 48

now.....

a + b = 9 + 48 = 57