2004 AMC 12B Problem 6

Attempt Problem 6 of the 2004 AMC 12B below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Minneapolis-St. Paul International Airport is

8

miles southwest of downtown St. Paul and

10

miles southeast of downtown Minneapolis. Which of the following is closest to the number of miles between downtown St. Paul and downtown Minneapolis?

13

14

15

16

17

Southwest and southeast directions are perpendicular

The distance is

\sqrt{10^2 + 8^2},

then estimate

Southwest and southeast are perpendicular, so the airport sits at the right angle of a right triangle with legs

8

and

10.

The distance between downtowns is

\sqrt{10^2 + 8^2} = \sqrt{164} \approx 12.8,

closest to

13.

Thus, the correct answer is A.

Problem 6 in other years