2003 AMC 12B 第 5 题

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：

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