swerve wrote:A boat travels due east for 3 kilometers, makes a right turn and heads due south for 12 kilometers, and finally makes a left turn and travels due east again for 6 more kilometers. What is the distance between the boat's starting and ending locations?
A. 10
B. 11
C. 13
D. 15
E. 17
The OA is D
Source: Princeton Review
Refer to the diagram above. We have to get the value of AE.
In ∆ABC and ∆CDE, we have
/_ABC = /_CDE = 90º;
/_ACB = /_DCE; Thus,
/_BAC = /_CED
Thus, ∆ABC and ∆CDE are similar triangles.
Thus, AB/BC = DE/CD => BC/CD = AB/DE = 3/6 = 1/2
We know that BD = 12 and BC/CD = 1/2, thus, BC = 12/3 = 4 and CD = 8
Applying Pythagoras theorem in ∆ABC, we have AC = √(AB^2 + BC^2) = √(3^2 + 4^2 = 5; similarly,
Applying Pythagoras theorem in ∆CDE, we have CE = √(CD^2 + DE^2) = √(8^2 + 6^2 = 10;
Thus, AE = AC + CE = 5 + 10 = 15
The correct answer:
D
Hope this helps!
-Jay
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