AMC8 2001

AMC8 2001 · Q16

AMC8 2001 · Q16. It mainly tests Area & perimeter, Transformations.

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?

一张边长4英寸的正方形纸张，沿垂直方向对折。然后两层纸都沿平行于折痕的方向切成两半。形成了三个新矩形，一个大的和两个小的。其中一个小矩形的周长与大矩形的周长之比是多少？

(A) $\frac{1}{3}$ $\frac{1}{3}$

(B) $\frac{1}{2}$ $\frac{1}{2}$

(D) $\frac{4}{5}$ $\frac{4}{5}$

(E) $\frac{5}{6}$ $\frac{5}{6}$

Answer

Correct choice: (E)

正确答案：（E）

Solution

The dimensions of the new rectangles are shown. The perimeter of a small rectangle is $4 + 1 + 4 + 1 = 10$ inches and for the large one it is $4 + 2 + 4 + 2 = 12$ inches. The ratio is $10/12 = 5/6$.

新矩形的尺寸如图所示。小矩形的周长是$4 + 1 + 4 + 1 = 10$英寸，大矩形的周长是$4 + 2 + 4 + 2 = 12$英寸。比值为$10/12 = 5/6$。

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