问题 解答题

王伟准备用一段长30米的篱笆围成一个三角形形状的小圈,用于饲养家兔,已知第一条边长为a米,由于受地势限制,第二条边长只能是第一条边长的2倍多2米。

(1)请用a表示第三条边长;

(2)问第一条边长可以为7米吗?请说明理由,并求出a的取值范围;

(3)能否使得围成的小圈是直角三角形形状,且各边长均为整数?若能,说明你的围法;若不能,说明理由。

答案

解:(1)∵第二条边长为2a+2,

∴第三条边长为30-a-(2a+2)=28-3a;

(2)当a=7时,三边长分别为7,16,7,

由于7+7<16,所以不能构成三角形,即第一条边长不能为7米,

可解得

即a的取值范围是

(3)在(2)的条件下,注意到a为整数,所以a只能取5或6,

当a=5时,三角形的三边长分别为5,12,13,由52+122=132知,恰好能构成直角三角形,

当a=6时,三角形的三边长分别为6,14,10,由62+102≠142知,此时不能构成直角三角形,

综上所述,能围成满足条件的小圈,它们的三边长分别为5米,12米,13米。

阅读理解

阅读理解。

     At the beginning of my 8:00 a.m. class one Monday at UNLV(拉斯维加斯内华达大学), 

I cheerfully asked my students how their weekend had been. One young man said that his

weekend had not been very good. The young man then proceeded to ask me why I always

seemed to be so cheerful.

     His question reminded me of something I'd read somewhere before: "Every morning when

you get up, you have a choice about how you want to approach life that day," I said to the

young man. "I choose to be cheerful."

     "Let me give you an example," I continued. "In addition to teaching here at UNLV, I also

teach out at the community college in Henderson. One day a few weeks ago I drove to

Henderson. I exited the freeway and turned onto College Drive. But just then my car died.

I tried to start it again, but the engine wouldn't turn over. So I put my flashers on, grabbed

my books, and marched down the road to the college."

     "As soon as I got there, the secretary in the Provost's office asked me what had happened.

'This is my lucky day', I replied, smiling."

     "Your car breaks down and today is your lucky day?" She was puzzled, "What do you

mean?"

     "I live seventeen miles from here. I replied. My car could have broken down anywhere

along the freeway. It didn't. Instead, it broke down in the perfect place: off the freeway, within

walking distance of here. I'm still able to teach my class, and I've been able to arrange for the

tow truck to meet me after class. If my car was meant to break down today, it couldn't have

been arranged in a more convenient fashion."

1. If you want to be cheerful you should ___________.

A. try to succeed in doing everything            

B. try to please your boss every day

C. earn a lot of money by working              

D. choose to be cheerful every day

2. The underlined phrase "turn over" in the third paragraph means "________"

A. roll over    

B. work normally    

C. stopped suddenly   

D. move around

3. According to this passage we can infer that the teacher's car broke down ____.

A. near UNLV          

B. along the highway

C. near Henderson        

D. at the community college

4. Which one of the following is TRUE?

A. The teacher taught not only at UNLV but also at the community college.

B. That was the teacher's lucky day because the teacher liked walking.

C. The teacher always hoped that the car would break down often.

D. The young man was sad because his car broke down.

单项选择题