题目内容
(2005•日照)某校数学课外活动探究小组,在老师的引导下进一步研究了完全平方公式.结合实数的性质发现以下规律:对于任意正数a、b,都有a+b≥2![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_ST/0.png)
A.120
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_ST/1.png)
B.60
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_ST/2.png)
C.120
D.60
【答案】分析:当一个四边形对角线长为a,b,且相互垂直时,其面积为:
.
解答:解:由题意得:
=3600,
则ab=7200,
所以有a+b≥2
,
即a+b≥120
.
故选A.
点评:此题是一道阅读理解类型题目,注意理解题目给出的条件,熟记对角线互相垂直的四边形的面积等于对角线乘积的一半是解题的关键.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_DA/0.png)
解答:解:由题意得:
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_DA/1.png)
则ab=7200,
所以有a+b≥2
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_DA/2.png)
即a+b≥120
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131021231929186312233/SYS201310212319291863122008_DA/3.png)
故选A.
点评:此题是一道阅读理解类型题目,注意理解题目给出的条件,熟记对角线互相垂直的四边形的面积等于对角线乘积的一半是解题的关键.
![](http://thumb2018.1010pic.com/images/loading.gif)
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