2004 AMC 12B Problems/Problem 6

Problem

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?

$(\mathrm {A}) 13\qquad (\mathrm {B}) 14 \qquad (\mathrm {C}) 15 \qquad (\mathrm {D}) 16 \qquad (\mathrm {E}) 17$

Solution

The directions "southwest" and "southeast" are orthogonal. Thus the described situation is a right triangle with legs 8 miles and 10 miles long. The hypotenuse length is $\sqrt{8^2 + 10^2} \sim 12.8$ , and thus the answer is $\mathrm{(A)}$ .

Without a calculator one can note that $8^2 + 10^2 = 164 < 169 = 13^2$ .

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2004 AMC 12B Problems/Problem 6

Problem

Solution