Question

what is the measure of x?

Explanation:

Step1: Use the geometric mean theorem

In a right - triangle, if a height is drawn to the hypotenuse, then the length of the height is the geometric mean of the lengths of the segments of the hypotenuse. Also, for the segments of the hypotenuse, we have the relationship \(6^{2}=4\times x\) (using the property of similar right - triangles formed by the altitude to the hypotenuse of a right - triangle).

Step2: Solve the equation for \(x\)

From \(6^{2}=4\times x\), we know that \(36 = 4x\). Then, divide both sides of the equation by 4: \(x=\frac{36}{4}=9\).

Answer:

9