1989 AMC 12 第 5 题

Question

用等长牙签搭成图示矩形网格。若网格高为

20

根牙签、宽为

10

根牙签，则共用了多少根牙签？

Toothpicks of equal length are used to build a rectangular grid as shown. If the grid is

20

toothpicks high and

10

toothpicks wide, then the number of toothpicks used is

30

200

410

420

430

分别计算水平和竖直牙签的数量

Count horizontal and vertical toothpicks separately

宽为

10

根牙签的网格有

11

条竖直网格线

A grid

10

toothpicks wide has

11

vertical grid lines

有

11

条竖直网格线，每条含

20

根牙签；有

21

条水平网格线，每条含

10

根牙签。总数为

11\cdot20+21\cdot10=430\text{。}

所以正确答案是 E。

There are

11

vertical grid lines with

20

toothpicks each, and

21

horizontal grid lines with

10

toothpicks each. The total is

11\cdot20+21\cdot10=430.

Thus the correct answer is E.

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