+436 Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 18,$ $BE = 20,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$
+129771 2A = BE * AC
2A = 20 * AC
2A/20 = AC
2A = AD * BC
2A = 18 * BC
2A/18 = BC
2A = CF * AB
2A / CF = AB
AC + BC > AB
2A/20 + 2A/18 > 2A/CF
1/20 + 1/18 > 1/CF
38 / 360 > 1/CF
19 / 180 > 1/CF
CF > 180 / 19 ≈ 9.47
Apparently CF has no max length.....it's min length = 10
Can someone else verify this ???
