# 2004 AMC 12B Problems/Problem 6

The following problem is from both the 2004 AMC 12B #6 and 2004 AMC 10B #8, so both problems redirect to this page.

## 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 $\sqrt{8^2 + 10^2}\approx12.8$, and thus the answer is $\boxed{\mathrm{(A)}\ 13}$.

Without a calculator one can note that $8^2+10^2=164<169=13^2\Rightarrow\boxed{\mathrm{(A)}\ 13}$.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 