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2010 AMC 10A Problem 7

Problem 7 of 25EasierGeometry

Crystal has a running course marked out for her daily run. She starts this run by heading due north for one mile. She then runs northeast for one mile, then southeast for one mile. The last portion of her run takes her on a straight line back to where she started. How far, in miles, is this last portion of her run?

Answer choices

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Solution

From the diagram, we see that the distance traveled is the hypotenuse of a right triangle. One of the legs is just 11 from running due north. The other leg is 12+12=2. \sqrt{1^2 + 1^2} = \sqrt2. The final distance is then 22+12=3. \sqrt{\sqrt2^2 + 1^2} = \sqrt3. Thus, C is the correct answer.

More practice

Concepts: Pythagorean Theorem · vector

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.