2008 AMC 10A 第 2 题

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

。正方形的面积占矩形面积的百分之多少？

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

设正方形边长为

s

，用

s

表示矩形的尺寸。

Let the square have side

s

and express the rectangle’s dimensions in terms of

s

矩形宽为

2s

，长为

4s

；将它的面积与

s^2

比较。

The rectangle is

2s

wide and

4s

long; compare its area to

s^2

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.

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