AMC10 2001 A

AMC10 2001 A · Q15

AMC10 2001 A · Q15. It mainly tests Area & perimeter, Ratios in geometry.

A street has parallel curbs 40 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is 15 feet and each stripe is 50 feet long. Find the distance, in feet, between the stripes.

一条街道有相距 40 英尺的平行路缘。一个由两条平行条纹界定的横道以一定角度穿过街道。条纹之间的路缘长度为 15 英尺，每条条纹长 50 英尺。求条纹之间的距离，单位英尺。

(A) 9 9

(B) 10 10

(D) 15 15

(E) 25 25

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) The crosswalk is in the shape of a parallelogram with base 15 feet and altitude 40 feet, so its area is $15\times 40=600\ \text{ft}^2$. But viewed another way, the parallelogram has base 50 feet and altitude equal to the distance between the stripes, so this distance must be $600/50=12$ feet.

（C）人行横道的形状是一个平行四边形，底为 15 英尺，高为 40 英尺，所以面积为 $15\times 40=600\ \text{ft}^2$。但换一种看法，这个平行四边形的底为 50 英尺，高等于条纹之间的距离，因此该距离必须是 $600/50=12$ 英尺。

Topics