Question

老式电视屏幕的宽高比为 $4:3$ 。也就是说，宽与高之比为 $4:3$ 。许多电影的宽高比不是 $4:3$ ，所以有时会以“宽银幕黑边”方式在电视屏幕上播放，也就是把屏幕顶部和底部等高的条带变暗，如图所示。假设一部电影的宽高比为 $2:1$ ，并在一台对角线为 $27$ 英寸的老式电视上播放。每条变暗条带的高度是多少英寸？

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：比与比例勾股定理矩形

难度评级：1410

解答：

因为屏幕为 $4:3$ ，对角线为 $27$ 英寸，所以 $h : w : 27 = 3 : 4 : 5$ ，得到高 $h = \dfrac{3}{5}\cdot 27 = 16.2$ ，宽 $w = \dfrac{4}{5}\cdot 27 = 21.6$ 。

点亮的 $2:1$ 区域使用完整宽度 $21.6$ ，高度为 $\dfrac{21.6}{2} = 10.8$ 。

两条黑边平分剩余高度，所以每条高度为 $\dfrac{16.2 - 10.8}{2} = 2.7$ 。

所以正确答案是 D。

Since the screen is $4:3$ with a $27$ -inch diagonal, $h : w : 27 = 3 : 4 : 5,$ giving height $h = \dfrac{3}{5}\cdot 27 = 16.2$ and width $w = \dfrac{4}{5}\cdot 27 = 21.6.$

The lit $2:1$ region has the full width $21.6$ and height $\dfrac{21.6}{2} = 10.8.$

The two strips share the remaining height, so each has height $\dfrac{16.2 - 10.8}{2} = 2.7.$

Thus, the correct answer is D.

2008 AMC 10A 第 14 题

答案：D

难度评级：1410

解答：

其他年份的第 14 题