Question 74
What is the ratio of the mean proportional between 4.5 and 0.5, and the third proportional to 4.5 and 9.0?
Solution
The mean is proportional between 4.5 and 0.5.
Mean proportion = $$\sqrt{\ 4.5\times\ 0.5}$$
= $$\sqrt{2.25}$$
= 1.5 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 = 18 Eq.(ii)
Ratio ==> Eq.(i) : Eq.(ii)
1.5 : 18
15 : 180
1 : 12
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