Given that "B", "D", and "F" are midpoints, you know that:
[tex]\begin{gathered} AC=50 \\ CE=60 \\ BD=35 \end{gathered}[/tex]
According to the Triangle Midsegment Theorem, the length of the segment that connects the midpoints of two sides of the triangle is half the length of the third side, and it is parallel to it.
In this case, since you need to find the length of BF, you can set up that:
[tex]BF=\frac{CE}{2}[/tex]
Then, you can substitute the length of CE into the equation and evaluate:
[tex]BF=\frac{60}{2}=30[/tex]
Hence, the answer is:
[tex]BF=30[/tex]
