Question

较老的电视屏幕宽高比为 $4:3$ 。也就是说，宽与高之比为 $4:3$ 。许多电影的宽高比不是 $4:3$ ，所以有时会用“信箱式”显示，也就是在屏幕顶部和底部加等高黑条，如图。假设一部电影宽高比为 $2:1$ ，在一台对角线为 $27$ 英寸的旧电视上播放。每条黑条的高度是多少英寸？

Older television screens have an aspect ratio of $4:3.$ That is, the ratio of the width to the height is $4:3.$ The aspect ratio of many movies is not $4:3,$ so they are sometimes shown on a television screen by “letterboxing” — darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of $2:1$ and is shown on an older television screen with a $27$ -inch diagonal. What is the height, in inches, of each darkened strip?

$2$

$2.25$

$2.5$

$2.7$

$3$

答案：D

知识点：勾股数比与比例

难度评级：1410

小提示：

屏幕宽、高、对角线成 $4:3:5$ 的比例。

The screen’s width, height, and diagonal are in ratio $4:3:5$

大提示：

电影画面使用完整宽度，高度等于宽度的一半。

The lit movie region keeps the full width but has height equal to half that width

解答：

屏幕高、宽、对角线成 $3:4:5$ ，所以高度为 $\tfrac{3}{5} \cdot 27 = 16.2$ 英寸，宽度为 $\tfrac{4}{5} \cdot 27 = 21.6$ 英寸。

电影宽高比为 $2:1$ ，使用完整宽度时高度为 $\tfrac{21.6}{2} = 10.8$ 英寸。

因此每条黑条的高度为 $\dfrac{16.2 - 10.8}{2} = 2.7$ 英寸。

所以正确答案是 D。

Since the sides and diagonal are in ratio $3:4:5,$ the height is $\tfrac{3}{5} \cdot 27 = 16.2$ inches and the width is $\tfrac{4}{5} \cdot 27 = 21.6$ inches.

The movie has aspect ratio $2:1,$ so its height is $\tfrac{21.6}{2} = 10.8$ inches.

Each darkened strip therefore has height $\dfrac{16.2 - 10.8}{2} = 2.7$ inches.

Thus, D is the correct answer.

2008 AMC 12A 第 9 题

答案：D

难度评级：1410

小提示：

大提示：

解答：

其他年份的第 9 题