题目内容

In the Rt△ABC,∠ACB=90°,AB+BC+CA=2+
6
,midline for hypotenuse(斜边)is 1,then AC?BC=
 
分析:根据告诉的斜边的中线的长为1,求得斜边的长,则两直角边的和等于
6
,然后设出一直角边的长,利用勾股定理得到方程,将两直角边求出来,计算它们的积即可.
解答:解:∵斜边的中线的长为1,
∴斜边AB的长为2,
∴BC+CA=2+
6
-AB=2+
6
-2=
6

设BC的长为x,则AC的长为
6
-x,
根据勾股定理得:x2+(
6
-x)2=22

整理得:x2-
6
x+1=0

∵BC+CA=
6

∴AC?BC=1,
故答案为1.
点评:本题考查了勾股定理的相关知识,同时题目中还应用到了一元二次方程根与系数的关系,是一道不错的综合考题.
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In England, people often talk about the weather because they can experience(经历)four seasons in one day.In the morning the weather is warm just like in spring.An hour later black clouds come and then it rains hard.The weather gets a little cold.In the late afternoon the sky will be sunny, the sun will begin to shine, and it will be summer at this time of a day.In England, people can also have summer in winter, or have winter in summer.So in winter they can swim sometimes, and in summer sometimes they should take warm clothes.When you go to England, you will see that some English people usually take an umbrella(伞)or a raincoat with them in the sunny morning, but you should not laugh at them.If you don't take an umbrella or a raincoat, you will regret(后悔)later in the day.

1.Why do people in England often talk about the weather?

A.Because they may have four seasons in one day.

B.Because they often have very good Weather.

C.Because the weather is warm just like in spring.

D.Because the sky is sunny all day.

2.From the story we know that when _______ come, there is a heavy rain.

A.sunshine and snow                               B.black clouds

C.summer and winter                                     D.spring and autumn

3."People can also have summer in winter." Means "it is sometimes too _______ in winter."

A.warm             B.cool                  C.cold              D.rainy

4.In the sunny morning some English people usually take a raincoat or an umbrella with them because _______.

A.their friends ask them to do so                  B.it often rains in England

C.they are going to sell them                      D.they are their favorite things

5.The best title(标题)for this passage is _______.

A.Bad Seasons                                 B.Summer or Winter

C.The Weather in England                      D.Strange English People

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