Question

一张正方形纸先对折。折好的纸再被一条与折痕平行的直线切成两半。展开后得到三个长方形：一个大的和两个小的。一个小长方形的周长与大长方形周长的比是多少？

A square piece of paper is folded in half. The folded paper is then cut in half by a straight cut parallel to the fold. This forms three rectangles: one large rectangle 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

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。

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

解答：

其他年份的第 24 题