2004 AMC 12B Problem 6

Below is the professionally curated solution for Problem 6 of the 2004 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12B solutions, or check the answer key.

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Concepts:Pythagorean Theoremestimation

Difficulty rating: 1190

6.

Minneapolis-St. Paul International Airport is 88 miles southwest of downtown St. Paul and 1010 miles southeast of downtown Minneapolis. Which of the following is closest to the number of miles between downtown St. Paul and downtown Minneapolis?

1313

1414

1515

1616

1717

Solution:

Southwest and southeast are perpendicular, so the airport sits at the right angle of a right triangle with legs 88 and 10.10. The distance between downtowns is 102+82=16412.8,\sqrt{10^2 + 8^2} = \sqrt{164} \approx 12.8, closest to 13.13.

Thus, the correct answer is A.

Problem 6 in Other Years