Question

Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.

Answer 1

Let a and b be the two numbers, whose mean proportional is 12.

∴ ab = 12²

`=>` ab = 144

`=> b = 144/a`  ...(i)

Now, third proportional is 96

∴ a : b :: b : 96

`=>` b² = 96a

`=> (144/a)^2 = 96a`

`=> (144)^2/a^2 = 96a`

`=> a^3 = (144 xx 144)/96`

`=>` a³ = 216 

`=>` a = 6

`b = 144/6 = 24`

Therefore, the numbers are 6 and 24.