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).