AMC12 2004 B

AMC12 2004 B · Q6

AMC12 2004 B · Q6. It mainly tests Pythagorean theorem, Coordinate geometry.

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?

明尼阿波利斯-圣保罗国际机场位于圣保罗市中心西南 $8$ 英里处，位于明尼阿波利斯市中心东南 $10$ 英里处。下列哪个选项最接近圣保罗市中心与明尼阿波利斯市中心之间的英里数？

(A) 13 13

(B) 14 14

(D) 16 16

(E) 17 17

Answer

Correct choice: (A)

正确答案：（A）

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 $8^2+10^2=164<169=13^2\Rightarrow\boxed{\mathrm{(A)}\ 13}$.

“西南”和“东南”的方向互相垂直。因此所描述的情形构成一条直角三角形，两条直角边分别长 $8$ 英里和 $10$ 英里。斜边长度为 $\sqrt{8^2 + 10^2}\approx12.8$，因此答案是 $\boxed{\mathrm{(A)}\ 13}$。不用计算器也可注意到 $8^2+10^2=164<169=13^2\Rightarrow\boxed{\mathrm{(A)}\ 13}$。

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