Two boats are drawn on a 14 by 15 grid. A small boat on the left is labeled A, and a bigger boat to the right is labeled B. A diagonal dashed line extends downward from boat A, and intersects with a vertical downward line from boat B, creating two triangles.

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?

(1 point)
Responses

12 miles
12 miles

28 miles
28 miles

14 miles
14 miles

25 miles

Answer 1

To solve this problem, we can use the properties of similar triangles and the midpoint theorem.

Since △ABC≅△EDC, we know that the corresponding sides are proportional. Let's call the length of BC as x. Then, the length of DC is also x.

Since C is the midpoint of AE, we can determine the length of AC. Since AB is 5 miles, and C is the midpoint of AE, AC = AE/2. Therefore, AC = 15 miles/2 = 7.5 miles.

Now, let's use the midpoint theorem. Since C is the midpoint of AE and DB, we know that BC = AC = 7.5 miles. Therefore, the length of DB is 2 * BC = 2 * 7.5 = 15 miles.

Therefore, the length of DB is approximately 15 miles.