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!
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.
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