SOLUTION: A triangle has vertices S(0,7), E(5,-6), and T(10,7). Find the length of the altitude to the shortest side.

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Question 176129: A triangle has vertices S(0,7), E(5,-6), and T(10,7). Find the length of the altitude to the shortest side.
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(6938) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle has vertices S(0,7), E(5,-6), and T(10,7). Find the length of the altitude to the shortest side.
drawing%28400%2C400%2C-3%2C12%2C-7%2C8%2Clocate%280%2C7.7%2C%27S%280%2C7%29%27%29%2Clocate%2810.3%2C7.7%2C%27T%2810%2C7%29%27%29%2Clocate%284.5%2C-6%2C%27E%285%2C-6%29%27%29%2C+%0D%0A%0D%0Agraph%28400%2C400%2C-3%2C12%2C-7%2C8%29%2C+triangle%284.7%2C-6%2C10%2C7%2C0%2C7%29%29

The altitude is a vertical line through E, so it has to 
have the same x-coordinate as E, that is, 5, and it is on 
the same level as S and T, so it has the same y-coordinate
as S and T, that is, 7.  

So we draw in the altitude EA(5,7):

drawing%28400%2C400%2C-3%2C12%2C-7%2C8%2Clocate%280%2C7.7%2C%27S%280%2C7%29%27%29%2Clocate%2810.3%2C7.7%2C%27T%2810%2C7%29%27%29%2Clocate%284.5%2C-6%2C%27E%285%2C-6%29%27%29%2C+line%285%2C-6%2C5%2C7%29%2C%0D%0Alocate%284.9%2C7.7%2C%27A%285%2C7%29%27%29%2C%0D%0Agraph%28400%2C400%2C-3%2C12%2C-7%2C8%29%2C+triangle%285%2C-6%2C10%2C7%2C0%2C7%29%29

So the altitute extends 6 units below the x-axis and 7
units above the x-axis, so the altitude EA is 6+7 or 13 
units in length

Edwin

Answer by MathTherapy(639) About Me  (Show Source):
You can put this solution on YOUR website!
square root of 219