AMC 8 2008 Problem 17
AMC8 2008 年第 17 题
四边形与多边形★★★☆☆
Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of 50 units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
Osborne 女士要求班级里的每一个学生都画一个周长为 50，且每条边长度都是整数的矩形。每个学生都计算了自己所画矩形的面积。那么这些矩形中，最大可能的面积和最小可能的面积的差是多少？
- A.76
- B.120
- C.128
- D.132
- E.136
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
A rectangle's area is maximized when its length and width are equivalent, or the two side lengths are closest together in this case with integer lengths. This occurs with the sides 12×13 = 156. Likewise, the area is smallest when the side lengths have the greatest difference, which is 1×24 = 24. The difference in area is 156-24=132.
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