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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 = 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.
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