Final answer:
Using the geometric mean property of the altitude drawn to the hypotenuse of right triangle ABC, we find that the length of segment AD is 3 units.
Step-by-step explanation:
Finding the Length of Segment AD in a Right Triangle
When dealing with a right triangle ABC, and an altitude BD is drawn to the hypotenuse AC creating two smaller right triangles ABD and BDC, we can apply geometric means and the Pythagorean Theorem to find the length of segment AD. Since BD = 6 and DC = 12, and triangle ADB is also a right triangle, we can use the geometric mean property which states:
- The length of the altitude (BD) squared is equal to the product of the two segments of the hypotenuse it creates (AD and DC). So, BD² = AD × DC.
This gives us the following equation: 6² = AD × 12. By simplifying, we get 36 = AD × 12. When we divide both sides by 12 to isolate AD, we get AD = 3. Therefore, the length of segment AD is 3 units.