Question

applying the geometric mean (altitude) theorem
what is the value of a?
36√2
8√3
9
6√2

Explanation:

Step1: Apply the geometric mean (altitude) theorem

The geometric mean (altitude) theorem states that in a right - triangle formed by an altitude \(a\) to the hypotenuse of a larger right - triangle, \(a=\sqrt{be}\), where \(b\) and \(e\) are the segments of the hypotenuse. Here, \(b = 18\) and \(e=4\).

Step2: Calculate the value of \(a\)

Substitute \(b = 18\) and \(e = 4\) into the formula \(a=\sqrt{18\times4}=\sqrt{72}\). Simplify \(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\).

Answer:

\(6\sqrt{2}\)