Question 1114027: In triangle ABC, length AB=32, length BC=10, and length AC=26. If line segment CH is the altitude to segment AB and segment CM is the median to AB, compute the length of line segment HM.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
1. Using the Heron's formula, calculate the area S of the triangle ABC.
The side lengths are given.
2. Next step find the length of the altitude CH from equation  = S.
3. Consider right-angled triangle AHC. In it, you know AC = 26.
In section 2 you just also found the length |CH|.
So you can find the leg |AH|.
3. Now you know |AM| (it is 16 units, half of |AB|).
You also know |AH|.
The difference |AB| minus |AH| is the length |MH| under the question.
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Answer by greenestamps(13209)  (Show Source):
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