1989 AMC 8 第 24 题

Question

把一张正方形纸沿竖直方向对折，再沿图中的虚线把折好的纸剪成两半。这样会得到三个长方形：一个大长方形和两个小长方形。一个小长方形的周长与大长方形周长之比是多少？

Suppose a square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed line. Three rectangles are formed—a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?

\dfrac{1}{2}

\dfrac{2}{3}

\dfrac{3}{4}

\dfrac{4}{5}

\dfrac{5}{6}

答案：E

知识点：折纸周长

难度评级：950

小提示：

可以假设原正方形边长为

4

Give the original square a convenient side length, such as

4,

and track the pieces

大提示：

含折痕的部分展开成一个

2 \times 4

的大长方形，另外两层各展开成一个

1 \times 4

的小长方形

The piece containing the fold unfolds to a

2 \times 4

large rectangle, while each other layer is a

1 \times 4

small rectangle

解答：

设原正方形边长为

4

。对折后得到一个

2 \times 4

的双层长方形，再用一条与折痕平行的线把折好的纸切开，分成含折痕的一条和不含折痕的一条。

含折痕的那块展开后是

2 \times 4

的大长方形，周长为

2(2 + 4) = 12

。另一块展开后成为两个

1 \times 4

的小长方形，每个周长为

2(1 + 4) = 10

。所求比为

\frac{10}{12} = \frac{5}{6}

。

所以正确答案是 E。

Let the square have side

4.

Folding in half makes a

2 \times 4

stack of two layers. Cutting parallel to the fold splits it into a strip containing the fold and a strip that does not.

The strip with the fold unfolds into the large rectangle,

2 \times 4,

with perimeter

2(2 + 4) = 12.

The other strip is two separate small rectangles, each

1 \times 4,

with perimeter

2(1 + 4) = 10.

The ratio is

\frac{10}{12} = \frac{5}{6}.

Thus, the correct answer is E .

1989 AMC 8 第 24 题

答案：E

难度评级：950

小提示：

大提示：

解答：

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