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Can someone please help me?

 

Triangle ABC has altitudes AD, BE, and CF. If AD = 12, BE = 14, and CF is a positive integer, then find the largest possible value of CF

 

Thanks!

 May 30, 2020
 #1
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Since the altitudes are inside the triangle, the triangle is acute.  This gives us the inequalities 12^2 + 14^2 > h^2, h^2 + 12^2 > 14^2, and h^2 + 14^2 > 12^2.  Then the largest h can be is 18.

 May 30, 2020

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