The mean proportional between 12 and a number is twice the mean proportional between 9 and 16. Find the number.
48
Mean proportional between 9 and 16: \(\sqrt{9 \times 16} = \sqrt{144} = 12\).
Twice this value: \(2 \times 12 = 24\).
Let the unknown number be \(x\). The mean proportional between 12 and \(x\) is \(\sqrt{12x}\), so \(\sqrt{12x} = 24\).
Squaring both sides: \(12x = 576\), so \(x = 48\).
Hence, the number is 48.
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Important Questions from Mean Proportional
What is the difference in the mean proportional between 1.8 and 3.2 and the third proportional to 5 and 3?
If x is subtracted from each of 23, 39, 32 and 56, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 4) and (3x + 1)?
When x is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x - 2) and (5x + 4)?
When x is subtracted from each of 21, 22, 60 and 64, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 1) and (7x + 8)?
When x is subtracted from each of 19, 28, 55 and 91, the numbers so obtained in this order, are in proportion. What is the mean proportional between (x + 9) and x 2?
