101k views
0 votes
In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD = 12 and DB=3. What is the length of h?

Only sides/angles known are
Base= 12+3,
Angle= Right angle/90°.
No clue how to solve this. I tried many methods. everyone who’s asked this question on here did not get a good answer. Please explain how it is done and what theorem is used.

In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also-example-1
User Holgac
by
8.2k points

1 Answer

0 votes

Answer:

h = 6

Explanation:

h is the short leg for AD in ΔADC: AD = 12

h is the long leg for DB in ΔCDB: DB = 3

Hence:

12/h = h/3

3 * 12/h = 3 * h/3 ==> isolate h by multiplying 3 on both sides

36/h = h

h * 36/h = h*h ==> multiply by h on both sides to remove fractions

36 = h^2

h =
√(36)

h = 6

User Ivan Ignatiev
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories