Applying the geometric mean theorem, the value of y is calculated as: y = 4√3 (option A).
What is the geometric mean theorem?
The geometric mean theorem, also known as the right triangle altitude theorem, establishes a connection between the altitude drawn on the hypotenuse of a right triangle and the two line segments it forms on the hypotenuse, stating that the altitude is equal to the geometric mean of these two segments.
Using this theorem, we can find y as follows:
y = √(4 * 12)
y = √48
y = √16 * √3
y = 4√3 (option A).