SOLUTION: 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 segme

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(52787) (Show Source): You can put this solution on YOUR website!
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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(13200) (Show Source): You can put this solution on YOUR website!

(1) Use Heron's formula to find the area of the triangle.

(2) Use the area of the triangle and the length of AB to find the length of CH.

(3) Use the lengths of CH and CB to find the length of BH.

(4) Use the lengths of BM and BH to find th length of HM.

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