△ABC≅△EDC and C is the midpoint of AE¯¯ and DB¯¯ . If Boat A is 5 miles from Boat B, and Boat A is 30 miles from an object at point E , then what is the length of DB¯¯ to the nearest mile?
14 miles
12 miles
28 miles
25 miles
Since triangle ABC is congruent to triangle EDC, we know that their sides are proportional.
AC/EC = BC/DC
Since C is the midpoint of AE and DB, we can say that AC = CE and BC = CD.
AC/EC = BC/DC
AC/30 = BC/5
AC = (30/5) * BC
AC = 6BC
Since AC = CE, we know that CE = 6BC.
CE + EC + DC = 30
6BC + BC + BC = 30
8BC = 30
BC = 30/8
BC ≈ 3.75
Since BC = CD, we know that CD ≈ 3.75.
DB = BC + CD
DB = 3.75 + 3.75
DB ≈ 7.5
Therefore, the length of DB is approximately 7.5 miles.
To the nearest mile, the length of DB is 8 miles.
However, this is not one of the given answer choices.