1. Because triangle ABC is a right triangle, it can be obtained from Pythagorean theorem: AC=5,

So the area of triangle ABC is 1/2*5* 12=30.

2. Because CD is the height on the side of AB, the area of right triangle ABC is 30.

So AB*CD* 1/2=30,

So CD=60/ 13.

3. The triangle ABE must be an obtuse triangle.

Because BE is the center line of the AC side,

So AB= 1/2*AC=5/2,

So the area of triangle ABE is 1/2*AB*BC= 15.

4. From the projective theorem, BD 2 = BF * BC.

That is 12 1= 12*BF,

So BF =12112,

Then in the right triangle BFD, the length of DF can be obtained by Pythagorean theorem (even here).