Question

一个正方形画在一个矩形内。矩形宽与正方形边长之比为 $2:1$ 。矩形长与宽之比为 $2:1$ 。矩形面积中有百分之多少在正方形内？

A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is $2:1.$ The ratio of the rectangle's length to its width is $2:1.$ What percent of the rectangle's area is inside the square?

$12.5$

$25$

$50$

$75$

$87.5$

答案：A

知识点：面积比百分数

难度评级：840

解答：

设正方形边长为 $s$ ，则正方形面积为 $s^2$ 。

矩形宽为 $2s$ ，长为 $2 \cdot 2s = 4s$ ，面积为 $8s^2$ 。

正方形占矩形面积的比例为 $\dfrac{s^2}{8s^2} = \dfrac{1}{8} = 12.5\%$ 。

所以正确答案是 A。

Let the side of the square be $s,$ so its area is $s^2.$

The width of the rectangle is $2s,$ and its length is $2 \cdot 2s = 4s,$ giving an area of $8s^2.$

The fraction inside the square is $\dfrac{s^2}{8s^2} = \dfrac{1}{8} = 12.5\%.$

Thus, the correct answer is A.

2008 AMC 10A 第 2 题

答案：A

难度评级：840

解答：

其他年份的第 2 题