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I need help with altitudes

 

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 7, 2023
 #1
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The answer is 65.

 Jun 7, 2023
 #2
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1/12  +  1/12 > 1/CF, solve for CF

 

CF > 6

 

Which means the minimum of 3rd altitude ==7.

 

Because the two given altitudes are 12 and 12, that means the triangle is an isosceles triangle. When the 2 altitudes are the same, the 3rd altitude has no " largest possible value", as long as the 3rd angle can be measured.

 Jun 7, 2023

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