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I need help with altitudes

 

Triangle ABC has altitudes AD, BE, and CF.  If AD = 12, BE = , and CF is a positive integer, then find the largest possible value of CF.

 Jun 3, 2023
 #1
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Answered yesterday.

 Jun 3, 2023
 #2
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Triangle ABC has altitudes AD, BE, and CF.  If AD = 12, BE = 12, and CF is a positive integer, then find the largest possible value of CF.

 Jun 3, 2023
 #3
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If the altitudes of the triangle are: AD=12  and  BE=12, then that means the triangle ABC is an isosceles triangle.

 

1/12 + 1/12 > 1/CF, solve for CF

 

CF > 6 

 

Which means the minimum altitude of CF = 7 and there is no ceiling for the largest possible value.

 Jun 4, 2023

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