Answer:
x = 3.5
Step-by-step explanation:
To find the altitude x of the given right triangle, we can use the Geometric Mean Theorem (Altitude Rule).
According to the Geometric Mean Theorem (Altitude Rule), the ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude:
[tex]\boxed{\sf \dfrac{Altitude}{Segment\;1}=\dfrac{Segment\; 2}{Altitude}}[/tex]
In this case, the altitude is x, and the two segments measure 2 and 6 units, respectively. Therefore:
[tex]\dfrac{x}{2}=\dfrac{6}{x}[/tex]
Cross-multiply:
[tex]x\cdot x = 6 \cdot 2\\\\\\x^2=12[/tex]
Square root both sides:
[tex]\sqrt{x^2}=\sqrt{12}\\\\\\x=3.4641016151...\\\\\\x=3.5\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x rounded to the nearest tenth is:
[tex]\LARGE\boxed{\boxed{x=3.5}}[/tex]
