配套习题- 利用构图法巧证不等式及最值问题 -【青果学院】

1/5单选题

难度：

1.

如图，在方格纸（每个小方格都是边长为1个单位长度的正方形）中，我们称每个小正方形的顶点为格点，以格点为顶点的图形称为格点图形，图中的△ABC为格点三角形，它的三边a，b，c的大小关系是（　　）

A	b＜c＜a
B	a＜c＜b
C	c＜b＜a
D	b＜a＜c

正确答案：Qw==

PGRpdj7op6PvvJrmoLnmja7lt7Lnn6XmoLzngrnkuInop5LlvaLvvIznlLHli77ogqHlrprnkIblvpc8L2Rpdj48ZGl2PuaJgOS7pTxpbWcgc3JjPSJodHRwczovL3AxLnFpbmdndW8uY29tL0cxL00wMC8wMS9GMy9yQkFDRkZNTmFYMlNjYWNJQUFBQ3pXQnh1QTAwMjUucG5nIiBkYXRhLWNrZS1zYXZlZC1zcmM9Imh0dHBzOi8vcDEucWluZ2d1by5jb20vRzEvTTAwLzAxL0YzL3JCQUNGRk1OYVgyU2NhY0lBQUFDeldCeHVBMDAyNS5wbmciIGhlaWdodD0iMjEiIHdpZHRoPSIxNzciPjwvZGl2PjxkaXY+4oi0Y++8nGLvvJxhLjwvZGl2Pg==

2/5单选题

难度：

2.

如图，将△ABC放在正方形网格图中（图中每个小正方形的边长均为1），点A，B，C恰好在网格图中的格点上，那么△ABC中BC的高是（）

A	√102
B	√104
C	√105
D	√5

正确答案：QQ==

PHA+PGltZyBzcmM9Imh0dHBzOi8vcDEucWluZ2d1by5jb20vRzEvTTAwLzA0LzNFL3JCQUNGRk1PN3Z1eUFuRXhBQUFSd0VUXzVKTTI4Mi5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMS5xaW5nZ3VvLmNvbS9HMS9NMDAvMDQvM0UvckJBQ0ZGTU83dnV5QW5FeEFBQVJ3RVRfNUpNMjgyLnBuZyIgYWx0PSIiIHN0eWxlPSJ3aWR0aDogMTU3cHg7IGhlaWdodDogMjQ0cHg7Ij48YnI+PC9wPg==

3/5单选题

难度：

3.已知a、b、c均为非负实数，求证：

下面有小明和小丽的解题思路，你赞同哪个？（）

A	小明：构造边长为a+b+c的正方形，根据两点之间线段最短的知识即可解答
B	小丽：尝试用平方去根号

正确答案：QQ==

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

4/5单选题

难度：

4.已知a，b均为正数，且a+b=2，则

的最小值为（）

A
B
C	13
D	23

正确答案：QQ==

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

5/5单选题

难度：

5.

设a、b、c、d为正实数，a＜b，c＜d，bc＞ad，有一个三角形的三边长分别为, 则此三角形的面积为（）

A
B
C
D

正确答案：QQ==

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