△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 △ABC and △EDC are congruent, we know that AB = ED.
Since C is the midpoint of AE and DB, we can conclude that AD = 2CD.
We also know that Boat A is 5 miles from Boat B, so AB = 5.
Combining these equations, we have:
ED = AB = 5
AD = 2CD
Using the Pythagorean Theorem, we can find the length of DB:
DB^2 = AD^2 + AB^2
DB^2 = (2CD)^2 + 5^2
DB^2 = 4CD^2 + 25
Since ED = AB = 5, CD = (ED / 2) = 5 / 2 = 2.5
Plugging this value back into the equation, we get:
DB^2 = 4(2.5^2) + 25
DB^2 = 4(6.25) + 25
DB^2 = 25 + 25
DB^2 = 50
Taking the square root of both sides, we find:
DB ≈ √50
DB ≈ 7.07
To the nearest mile, the length of DB is 7 miles. Therefore, the answer is not one of the given options.