Multiple choice

What is the ratio of mean proportional between 3.6 and 12.1 and third proportional between 2 and 11?

  1. 36 : 5

  2. 6 : 5

  3. 11 : 36

  4. 6 : 55

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D Correct answer
Explanation

Mean proportional between 3.6 and 12.1 is sqrt(3.6 * 12.1) = sqrt(43.56) = 6.6. Third proportional to 2 and 11 is x where 2/11 = 11/x, so x = 121/2 = 60.5. Ratio = 6.6 / 60.5 = 66 / 605 = 6 / 55.

AI explanation

The mean proportional between 3.6 and 12.1 is the square root of their product, which is the square root of 43.56, yielding 6.6. The third proportional between 2 and 11 is 11 times 11 divided by 2, which equals 60.5. The ratio of the mean proportional to the third proportional is 6.6 to 60.5. Converting this to a whole number ratio by multiplying by 10 and simplifying gives 66 to 605, which reduces to 6 to 55.