The mean proportional between two positive numbers is 30. If the difference between the two numbers is 45, what is the smaller of the two numbers?

If \(x\) is the mean proportional between \((a+b)\) and \((a-b)\), then find the value of \(x\).

In a fitness park, a straight walking path is divided into three consecutive segments. The lengths of the first and third segments are 18 m and 50 m respectively. If the length of the middle segment is the mean proportional between the other two, what is its length?

If the height at which a ladder touches the wall is the mean proportional between 6 meters and 24 meters, at what height does the ladder touch the wall?

A rectangular garden has a length of 16 meters and a width of x meters. If the width is the mean proportional between 4 meters and 64 meters, what is the value of x?

The mean proportional between 12 and a number is twice the mean proportional between 9 and 16. Find the number.

Find the mean proportional between \((2+\sqrt{3})\) and \((10-\sqrt{75})\).

Two positive numbers differ by 20. The mean proportional between these two numbers is 24. What is the sum of these two numbers?

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)?