Question

In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD = 4 and DB = 16. What is the length of the altitude CD?

1) 8
2) 12
3) 16
4) 20

Answer 1

To find the length of the altitude CD, we can use the property of similar triangles. By setting up the proportion CD/AD = DB/AB and solving for h, we find that the length of the altitude CD is 16/3. Therefore, the correct answer is 20.

Step-by-step explanation:

To find the length of the altitude CD, we can use the property of similar triangles. Since triangle ABC is a right triangle, the altitude CD will divide the hypotenuse AB into two segments, AD and DB. We know that AD = 4 and DB = 16. Let the length of CD be h. By using the property of similar triangles, we can set up the proportion:

CD/AD = DB/AB

Substituting the given values and h for CD, we get:

h/4 = 16/(4 + h)

Cross multiplying the proportion, we get:

4h = 16(4 + h)

Simplifying the equation, we have:

4h = 64 + 16h

12h = 64

h = 64/12

h = 16/3

Therefore, the length of the altitude CD is 16/3, which is equal to approximately 5.333. Therefore, the correct answer is 4) 20.