2011 AMC 10B 第 3 题

Question

在一家商店中，若长度标为

x

英寸，则实际长度至少为

x - 0.5

英寸，至多为

x + 0.5

英寸。若一个长方形瓷砖的尺寸标为

2

英寸乘

3

英寸，则它的最小面积是多少平方英寸？

At a store, when a length is reported as

x

inches that means it is at least

x - 0.5

inches and at most

x + 0.5

inches. Suppose the dimensions of a rectangular tile are reported as

2

inches by

3

inches. In square inches, what is the minimum area for the rectangle?

3.75

4.5

5

6

8.75

使用最小可能的长和宽。

Use the smallest possible length and width

标为

2

乘

3

的瓷砖最小可为

1.5

乘

2.5

。

The reported

2

by

3

tile can be as small as

1.5

by

2.5

最小可能尺寸为

1.5\times 2.5

，所以面积为

1.5\cdot 2.5=3.75\text{。}

所以正确答案是 A。

The smallest possible dimensions are

1.5\times 2.5,

so the area is

1.5\cdot 2.5=3.75.

Thus, the correct answer is A .

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