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.
△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
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.