Question

一张边长 $4$ 英寸的正方形纸沿竖直方向对折。然后将两层纸沿平行于折痕的方向切成两半。形成三个新的长方形：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之比是多少？

A square piece of paper, $4$ inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new 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?

$\dfrac{1}{3}$

$\dfrac{1}{2}$

$\dfrac{3}{4}$

$\dfrac{4}{5}$

$\dfrac{5}{6}$

答案：E

知识点：折纸周长

难度评级：1350

解答：

正方形对折后形成一个 $4\times2$ 的长方形。

将折叠后的纸沿平行于折痕的方向切成两半，得到两个 $4\times1$ 的小长方形和一个 $4\times2$ 的大长方形。

一个小长方形周长与大长方形周长之比为 $\frac{2(4+1)}{2(4+2)}=\frac{10}{12}=\frac56.$

所以正确答案是 E。

The square is folded in half to create a $4\times2$ rectangle.

Cutting the folded paper in half parallel to the fold gives two small $4\times1$ rectangles and one large $4\times2$ rectangle.

The ratio of the perimeter of a small rectangle to the perimeter of the large rectangle is $\frac{2(4+1)}{2(4+2)}=\frac{10}{12}=\frac56.$

Thus, E is the correct answer.

2001 AMC 8 第 16 题

答案：E

难度评级：1350

解答：

其他年份的第 16 题