Question

1. solve for x.

10.5
6√3
20
10

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle, if an altitude is drawn from the right - angle to the hypotenuse, then the length of the altitude is the geometric mean between the lengths of the two segments of the hypotenuse. Also, the square of the length of a leg is equal to the product of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.
Let the hypotenuse be \(3 + 9=12\). We know that for the leg \(x\), \(x^{2}=9\times(3 + 9)\).

Step2: Calculate \(x\)

\[

$$\begin{align*} x^{2}&=9\times12\\ x^{2}& = 108\\ x&=\sqrt{108}\\ x& = 6\sqrt{3} \end{align*}$$

\]

Answer:

B. \(6\sqrt{3}\)