2004 AMC 12B Problem 6

Problem 6 of 25EasierGeometry Arithmetic

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?

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Solution

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.

Tagged: Pythagorean Theorem · estimation