in the figure below, find the exact value of x. (do not approximate your answer.)

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle, if an altitude is drawn from the right - angle to the hypotenuse, then (x^{2}=4\times6).

Step2: Solve for (x)

Take the square root of both sides. Since (x) represents a length, we consider the positive square root. So (x = \sqrt{24}=2\sqrt{6}).

Answer:

(2\sqrt{6})