Question

In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD = 8 and DB = 2. What is the value of h? (units)

Answer 1

The length of the altitude CD (h) in right triangle ABC can be found using the geometric mean property, leading to h being 4 units.

Step-by-step explanation:

In right triangle ABC, the altitude CD is drawn to the hypotenuse AB. We are given that AD = 8 units, DB = 2 units, and we need to find the length of the altitude, CD, which we'll refer to as h. To solve for h, we can apply the geometric mean property of the altitude of a right triangle, which states that the length of the altitude is equal to the geometric mean of the segments it divides the hypotenuse into. This gives us two equations:

• h² = AD × DB
• h² = 8 × 2
• h² = 16

Now, taking the square root of both sides, we get:

• h = √16
• h = 4 units