Question

许多电视屏幕是长方形，并用对角线长度来标记尺寸。标准电视屏幕的水平长度与高度之比为 $4 : 3$ 。一台“ $27$ 英寸”电视的水平长度最接近下列多少英寸？

Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is $4 : 3.$ The horizontal length of a “ $27$ -inch” television screen is closest, in inches, to which of the following?

$20$

$20.5$

$21$

$21.5$

$22$

答案：D

知识点：勾股数比与比例

难度评级：1000

小提示：

长、宽和对角线的比例为 $4 : 3 : 5$ 。

The length, height, and diagonal are in the ratio $4 : 3 : 5$

大提示：

对角线对应 $5$ 份且等于 $27$ ，所以水平长度是 $27$ 的 $\tfrac{4}{5}$ 。

The diagonal corresponds to $5$ parts and equals $27,$ so the length is $\tfrac{4}{5}$ of $27$

解答：

因为长高比为 $4:3$ ，长、高、对角线组成 $4:3:5$ 的直角三角形。对角线长为 $27$ ，所以水平长度为 $\dfrac{4}{5}(27)=21.6\text{，}$ 最接近 $21.5$ 。

所以正确答案是 D。

Since the length and height are in ratio $4:3,$ the length, height, and diagonal form a $4:3:5$ right triangle. The diagonal is $27,$ so the horizontal length is $\dfrac{4}{5}(27)=21.6,$ which is closest to $21.5.$

Thus, the correct answer is D.

2003 AMC 10B 第 6 题

答案：D

难度评级：1000

小提示：

大提示：

解答：

其他年份的第 6 题