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I need help with altitudes
Triangle ABC has altitudes AD, BE, and CF. If AD = 12, BE = 18, and CF is a positive integer, then find the largest possible value of CF.

 May 23, 2023
 #1
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Hello,

To find the largest possible value of CF, we need to consider the relationship between altitudes and sides of a triangle. By using the formula CF = 2 * area(ABC) / AB, the largest possible value of CF occurs when AB is minimized. Therefore, CF will be maximum when AB is minimized to its smallest possible value.

 

Best regard,

MyCenturaHealth

 May 23, 2023
 #2
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H = 1/2 (1/CF + 5/36), 

   
1/1100=4 * sqrt[H * (H-1/12)*(H-1/18)*(H-1/CF)], solve for H, CF


H=0.0837303
CF ==35 - largest possible altitude

 May 23, 2023

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