AMC8 2006

AMC8 2006 · Q10

AMC8 2006 · Q10. It mainly tests Functions basics, Coordinate geometry.

Jorge's teacher asks him to plot all the ordered pairs $(w, l)$ of positive integers for which $w$ is the width and $l$ is the length of a rectangle with area 12. What should his graph look like?

Jorge 的老师让他绘制所有正整数有序对 $(w, l)$，其中 $w$ 是矩形的宽度，$l$ 是长度，面积为 12。他的图形应该是什么样的？

(A)

(B)

(C)

(D)

(E)

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) When the area of a rectangle is 12 square units and the sides are integers, the factors of 12 are the possible lengths of the sides. In point form, the side lengths could be (1, 12), (2, 6), (3, 4), (4, 3), (6, 2) and (12, 1). Only graph A fits these points.

（A）当一个长方形的面积为 12 平方单位且边长为整数时，12 的因数就是边长可能的取值。用点的形式表示，边长可以是 (1, 12)、(2, 6)、(3, 4)、(4, 3)、(6, 2) 和 (12, 1)。只有图 A 符合这些点。

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