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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