What is the ratio of the mean proportional between 4.5 and 0.5, and the third proportional to 4.5 and 9.0?
The mean is proportional between 4.5 and 0.5.
Mean proportion = $$\sqrt{\ 4.5\times\ 0.5}$$
=Â $$\sqrt{2.25}$$
= 1.5Â Â Eq.(i)
Third proportional to 4.5 and 9.0.
Let's assume the third proportion is 't'.
4.5 : 9 :: 9 : t
$$4.5t = 9\times9$$
$$t = 2\times9$$
t = 18Â Â Â Eq.(ii)
Ratio ==>Â Eq.(i) :Â Eq.(ii)
1.5 : 18
15 : 180
1 : 12
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