Question

Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.

Answer 1

Let the required number be a and b.

Given, 14 is the mean proportional between a and b.

`=>` a : 14 = 14 : b

`=>` ab = 196

`=> a = 196/b` ...(1)

Also, given, third proportional to a and b is 112.

`=>` a : b = b : 112

`=>` b² = 112a  ...(2)

Using (1), we have

`b^2 = 112 xx 196/b`

b³ = (14)³(2)³

b = 28

From (1),

a = `196/28` = 7

Thus, the two numbers are 7 and 28.