Question

defination of contunuid proportion​

Answer 1

b : : b : c

⇒ Product of extremes = Product of means

⇒ a x c = b x b

⇒ a x c = b 2

Continued-proportion is also known as mean proportional .

If ‘b’ is a mean proportional between a and c then b 2 = ac.

Examples :

1) Find the mean proportional between 9 and 25.

Solution :

Let x be the mean proportional between 9 and 25.

⇒ x 2 = 9 x 25

⇒ x 2 = 225

⇒ x = 15

Hence, the mean proportional between 9 and 25 is 15.

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2) If 3, x , 12 are in continued-proportion, find the value of x.

Solution :

Since 3,x,12 are in continued-proportion,

3,x,x,12 are in proportion.

Product of extremes = Product of means

⇒ 3 x 12 = x . x

⇒ 36 = x 2

⇒ x = 6.