SOLUTION: Altitude drawn to the hypotenuse of a right triangle divides hypotenuse into segments of length 2 & 16. Then A) the altitude measures 4 B) the altitude measures 6 C) one le

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Question 839850: Altitude drawn to the hypotenuse of a right triangle divides hypotenuse into segments of length 2 & 16. Then
A) the altitude measures 4
B) the altitude measures 6
C) one leg measures 4
D) one leg measures 6
I don�t know how to do this question. It would be helpful if you could show me the proportion that you set up or any work that helped you gained this answer. Thanks
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
what you are dealing with is the mean proportional theorem or what is also called the hypotenuse-altitude theorem or something like that.
a good reference can be found here:
http://www.regentsprep.org/Regents/math/geometry/GP12/LMeanP.htm

in your problem, the solution is that one leg measure 6.

here's a picture of your triangle as best I can construct it.

the ratios that can be formed are shown in the diagram.

the ratio that gives you the solution is the middle ratio.

check out the link.
it's pretty good in explaining what is going on.
what makes the ratios work is that the 3 triangles formed are all similar to each other which means their corresponding sides are proportional.