Question

1. find the value of x. 6√3 6 4 2√3

Explanation:

Step1: Apply geometric mean theorem

In a right - triangle, if an altitude is drawn to the hypotenuse, then the altitude is the geometric mean between the segments of the hypotenuse. Also, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to that leg. For the leg $x$, we have the formula $x^{2}=3\times(9 + 3)$.

Step2: Calculate the value of $x^{2}$

$3\times(9 + 3)=3\times12 = 36$. So $x^{2}=36$.

Step3: Solve for $x$

Taking the square - root of both sides, since $x$ represents the length of a side of a triangle and must be positive, $x=\sqrt{36}=6$.

Answer:

6