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The perimeter of a rectangle is 40. What is the greatest area of the rectangle?A
The perimeter of a rectangle is 40. What is the greatest area of the rectangle?A
游客
2024-01-13
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问题
The perimeter of a rectangle is 40. What is the greatest area of the rectangle?
选项
A、120
B、80
C、60
D、100
E、40
答案
D
解析
设矩形的长和宽分别为a和b,那么2(a+b)=40,a+b=20,现在求面积ab的最大值。由于两个数的算术平均值大于等于两个数的几何平均值,(a+b)/b≥
,因此
≤10,ab的最大值为100。
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