I need help with altitudes

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

Answered yesterday.

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.

If the altitudes of the triangle are: AD=12 and BE=12, then that means the triangle ABC is an isosceles triangle.

1/12 + 1/12 > 1/CF, solve for CF

CF > 6

Which means the minimum altitude of CF = 7 and there is no ceiling for the largest possible value.