Question

许多电视屏幕是用对角线长度来度量的长方形。标准电视屏幕的水平长度与高度之比为 $4 : 3$ 。一台 $27$ 英寸电视屏幕的水平长度最接近下列哪一个数，单位为英寸？

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：1050

小提示：

若边长比为 $4 : 3$ ，则高度、水平长度和对角线之比为 $3 : 4 : 5$

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

大提示：

对角线为 $27$ ，所以水平长度是 $27$ 的 $\dfrac{4}{5}$

The diagonal is $27,$ so the horizontal length is $\dfrac{4}{5}$ of $27$

解答：

边长比为 $4 : 3$ 的长方形，其高度、水平长度和对角线之比为 $3 : 4 : 5$ 。对角线为 $27$ ，所以水平长度为 $\frac{4}{5}(27) = 21.6\text{，}$ 最接近 $21.5$ 。

因此，正确答案是 D。

A rectangle with side ratio $4 : 3$ has height, length, and diagonal in ratio $3 : 4 : 5.$ With diagonal $27,$ the horizontal length is $\frac{4}{5}(27) = 21.6,$ which is closest to $21.5.$

Thus, the correct answer is D.

2003 AMC 12B 第 5 题

答案：D

难度评级：1050

小提示：

大提示：

解答：

其他年份的第 5 题