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
Let h be the third altitude. Then by the triangle inequality, h + 12 > 14, h + 14 > 12, and 12 + 14 > h. The largest integer h that satisfies these inequalities is h = 25.