1999 AMC 8 第 5 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
5.
一个长 英尺、宽 英尺的长方形花园被栅栏围住。为了在使用同样栅栏的情况下扩大花园，花园改成正方形。面积增加了多少平方英尺？
A rectangular garden feet long and feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?
小提示：
周长保持不变
Keep the perimeter the same
大提示：
正方形边长是原周长的四分之一
The square side length is one-fourth of the old perimeter
解答：
当前栅栏的周长为 英尺。如果四条边都相等，那么每条边长为 英尺。因此正方形面积为 平方英尺。原花园面积为 平方英尺。
因此面积差是 平方英尺。
所以正确答案是 D。
The current length of the fence is feet. If all the sides become the same, then each side length is feet. As such, the area of the square is then square feet. Note that the original area of the garden is square feet.
Therefore, the difference is square feet.
Thus, D is the correct answer.
其他年份的第 5 题
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