△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? (1 point) Responses 14 miles 14 miles 12 miles 12 miles 28 miles 28 miles 25 miles
From the given information, we know that △ABC and △EDC are congruent triangles. Since C is the midpoint of AE¯¯¯¯¯¯¯¯ and DB¯¯¯¯¯¯¯¯, we can say that DC¯¯¯¯¯¯¯¯=DB¯¯¯¯¯¯¯¯=x.
Now, let's analyze the given distances. Boat A is 5 miles from Boat B, and Boat A is 30 miles from an object at point E. Since C is the midpoint of AE¯¯¯¯¯¯¯¯, we can deduce that DE¯¯¯¯¯¯¯¯=2(30)=60 miles.
Using the congruent triangles, we can say that DC¯¯¯¯¯¯¯¯=x=DE¯¯¯¯¯¯¯¯=60 miles.
Therefore, the length of DB¯¯¯¯¯¯¯¯ is 60 miles to the nearest mile.