#### Question

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

#### Solution

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

`∴ ab = 12^2 => ab = 144 => 144/a` ....(1)

Now third proportional is 96

∴ a : b : : b : 96

`=> b^2 = 96a`

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

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

`=> a^3 = 216`

`=> a = 6`

`b = 144/6 = 24`

Therefore the number are 6 and 24.

Is there an error in this question or solution?

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Find Two Numbers Such that the Mean Mean Proportional Between Them is 12 and the Third Proportional to Them is 96. Concept: Proportions.

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