What is the ratio of the mean proportional between 4.5 and 0.5, and the third proportional to 4.5 and 9.0?

1 : 12

Mean proportion = \(\sqrt {4.5 x 0.5 }\)

⇒ \(\sqrt {2.25 }\) = \(\frac{15}{10}\) = \(\frac{3}{2}\)

The third proportional a,

⇒ 4.5 : 9.0 : a

⇒ 4.5a = 9 x 9

⇒ a = 18.

Ratio MP : Third proportional = \(\frac{3}{2}\) : 18 = 3 : 36 = 1 : 12.