AMC10 2011 B

AMC10 2011 B · Q3

AMC10 2011 B · Q3. It mainly tests Rounding & estimation, Area & perimeter.

At a store, when a length is reported as x inches that means the length 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?

在一家商店，当长度报告为 x 英寸时，意味着长度至少为 x − 0.5 英寸，至多为 x + 0.5 英寸。假设一块矩形瓷砖的尺寸报告为 2 英寸乘 3 英寸。矩形的最小面积是多少平方英寸？

(A) 3.75 3.75

(B) 4.5 4.5

(D) 6 6

(E) 8.75 8.75

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The smallest possible width for the rectangle is 2 − 0.5 = 1.5 inches. Similarly the smallest possible length is 2.5 inches. Hence the minimum area is (1.5)(2.5) = 3.75 square inches.

答案 (A)：矩形的最小可能宽度是 2 − 0.5 = 1.5 英寸。同样，最小可能长度是 2.5 英寸。因此，最小面积是 (1.5)(2.5) = 3.75 平方英寸。

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