Various+Problem

These are some problems that I love, and some that are really really bothering me.

1. We'll start with one that's really really bothering me. This problem made me THINK. Time for your brain to hurt.... =)

I am taking a guess that triangle BFD is similar to triangle EFA and that triangle ABD is similar to triangle EGA. Is that right? If so, then the proportion between triangles BFD and EFA should equal to to the proportion between triangles ABD and EGA. Go with it, show your work, and let's see what happens. BTW- who are you? PLEASE sign your name guys! :)

I like candy corn-Aaron Walker

2. And now an easier one...... Given a triangle with side lengths 15, 20, and 25, find the length of the shortest altitude. WORK and picture!