Question

△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

Answer 1

pick one of the answer i have up there

Answer 2

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.

Answer 3

Based on the given answer choices, the length of DB¯¯ to the nearest mile would be 14 miles.