Answer:
AB = 5
EF = 12.5
BF = 6
Step-by-step explanation:
Use the Pythagorean theorem to find AB.
(AD)² + (BD)² = (AB)²
3² + 4² = (AB)²
(AB)² = 25
AB = 5
Use similar triangles to find EF.
DA/AB = DE/EF
3/5 = 7.5/EF
3 × EF = 5 × 7.5
EF = 12.5
Use side splitting to find BF.
DA/AE = DB/BF
3/(7.5 - 3) = 4/BF
3/4.5 = 4/BF
3 × BF = 4 × 4.5
BF = 6
