The fourth proportional to 16, a and 9a is 324. What is the value of a?

Correct option is C

Given:

The numbers are 16, a, and 9a, and the fourth proportional is 324.

Formula Used:

The formula for the fourth proportional is:

​$$\frac{a}{b} = \frac{c}{d}$$​​

Where a, b, c, d are in proportion.

Solution:

a = 16, b = a, c = 9a, and d = 324

Using the formula for the fourth proportional:

​$$324 = \frac{a \times 9a}{16} \\ \ \\324 = \frac{9a^2}{16} \\ \ \\324 \times 16 = 9a^2 \\ \ \\5184 = 9a^2 \\ \ \\a^2 = \frac{5184}{9} = 576 \\ \ \\a = \sqrt{576} = 24$$​​