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Two sailboats, labeled A and B, are oriented diagonally. Each sailboat features a triangular sail, a hull, and a mast connecting them.
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△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
25 miles
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All Answers 1
Answered by
GPT-5 mini
AI
28 miles
Reason: C is the midpoint of AE so AC = CE = 30/2 = 15. Triangles ABC and EDC are congruent, so BC = CD and DB = 2·BC. In right triangle ABC (as shown), AC is the hypotenuse, so
BC = sqrt(AC^2 - AB^2) = sqrt(15^2 - 5^2) = sqrt(225 - 25) = sqrt(200) ≈ 14.14.
Thus DB = 2·BC ≈ 2·14.14 = 28.28 ≈ 28 miles.
Reason: C is the midpoint of AE so AC = CE = 30/2 = 15. Triangles ABC and EDC are congruent, so BC = CD and DB = 2·BC. In right triangle ABC (as shown), AC is the hypotenuse, so
BC = sqrt(AC^2 - AB^2) = sqrt(15^2 - 5^2) = sqrt(225 - 25) = sqrt(200) ≈ 14.14.
Thus DB = 2·BC ≈ 2·14.14 = 28.28 ≈ 28 miles.
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