If 48:x::x:75, and x>0, then what is the value of x ?

Correct option is D

Given:

$$\frac{48}{x} = \frac{x}{75} \\ \\$$

Concept Used:

In a proportion, the product of the means equals the product of the extremes.

Solution:

​$$\text{Using this property:} \\\ \\48 \cdot 75 = x \cdot x \\\ \\48 \cdot 75 = x^2 \\\ \\x^2 = 3600 \\\ \\x = \sqrt{3600} = \pm60 \\\ \\\text{Since } x > 0, \text{ the solution is:} \\\ \\x = 60 \\ \\$$​​