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What is the ratio of the mean proportional of 1.21 and 0.09 to the mean proportional of 0.16 and 0.36?

1. 11: 8
2. 13: 8
3. 13: 12
4. 11: 13

Correct answer: 11: 8

Solution

The mean proportional of 1.21 and 0.09 is $\sqrt{1.21\times 0.09}=\sqrt{0.1089}=0.33$. The mean proportional of 0.16 and 0.36 is $\sqrt{0.16\times 0.36}=\sqrt{0.0576}=0.24$. Their ratio is $0.33:0.24=33:24=11:8$.

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