Question

what is the value of a? 6√2 9 8√3 36√2

Explanation:

Step1: Use the geometric mean theorem (altitude-on-hypotenuse theorem)

In a right - angled triangle, if an altitude is drawn to the hypotenuse, then the length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse. Here, we assume the larger triangle has some right - angled properties (by the right - angle markings). The formula is \(a=\sqrt{18\times4}\).

Step2: Simplify the square root

$$
LATEXBLOCK0
$$

Answer:

\(6\sqrt{2}\)