Question

What is value of x if 64, x and 1 are in continued proportion

Answer 1

Since 64 , x , and 1 are in continued proportion then

64 : x :: x : 1

if a : b = b : c i.e. a/b = b/c i.e. b² = ac

if a , b , c are in continuous proportion then the middle term b is called the mean proportion between 'a' and 'c' , 'a' is the first proportion and 'c' is the third proportion

Thus , if b is the mean proportion between 'a' and 'c'

then b² = ac i.e. b = √(ac)

⇒ x² = 64 × 1

⇒ x = √64

Hence the middle term = 8

Answer 2

Answer:

Value of x is 8

Step-by-step explanation:

What is Continued Proportion?

Three quantities are said to be in continued proportion, if the ratio of first and second is equal to ratio of second and third. The middle term (second quantity) is called mean proportional between first and third quantities.

If x, y and z are in continued proportion,

$x : y :: y : z \\ = > x : y = y: z$  

In continued proportion, square of the middle term is equal to the product of other two quantities. i.e, if $x : y = y: z$ then,

$xz = y^{2}$

Given:

64, x and 1 are in continued proportion. It can be written as,

$64 : x = x : 1\\\\= > \frac{64}{x} = \frac{x}{1} \\\\= > 64 \times 1 = x \times x\\\\= > x^{2} = 64\\\\= > x = \sqrt{64}\\\\= > x = 8$

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