首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
A flat rectangular picture, represented by the unshaded region in the figure above, is mounted in a flat rectangular frame, repr
A flat rectangular picture, represented by the unshaded region in the figure above, is mounted in a flat rectangular frame, repr
admin
2014-08-13
66
问题
A flat rectangular picture, represented by the unshaded region in the figure above, is mounted in a flat rectangular frame, represented by the shaded region. The frame is 1 inch wide on all sides. For what value of x, in inches, is the area of the frame equal to the area of the picture?
选项
A、4
B、5
C、6
D、7
E、8
答案
C
解析
In this question, you are asked to determine the value of x for which the area of the frame is equal to the area of the picture. To do this, you need to express both the area of the frame and the area of the picture in terms of x and then find the value of x for which the two expressions are equal.
The area of the picture is the area of the inner rectangle, and the area of the frame is the area of the outer rectangle minus the area of the inner rectangle. Since the area of a rectangle is the length times the width, you need to know the length and width of the inner and outer rectangles.
In the figure, you are given that the length of the inner rectangle is x inches, but the width is not given. However, since you know that the width of the frame is 1 inch, it follows that the width of the inner rectangle is equal to the width of the outer rectangle minus 2 inches, or x - 2 inches. Thus, the area of the inner rectangle is x(x — 2)square inches.
In the figure, you are given that the width of the outer rectangle is x inches, but the length is not given. However, since you know that the width of the frame is 1 inch, it follows that the length of the outer rectangle is equal to the length of the inner rectangle plus 2 inches, or x + 2 inches. Thus, the area of the outer rectangle is x(x + 2)square inches.
Since the area of the frame is the area of the outer rectangle minus the area of the inner rectangle, the area of the frame is x(x + 2)- x(x - 2)= x
2
+ 2x - x
2
+ 2x = 4x square inches.
Now you are ready to set up the equation. Set the expression for the area of the picture equal to the expression for the area of the frame and solve the resulting equation for x, as follows.
x(x - 2)= 4x
x
2
- 2x = 4x
x
2
- 6x = 0
x(x - 6)= 0
There are two solutions to the equation, x = 0 and x = 6. Since x represents the length of a picture, in inches, the solution x = 0 does not make sense in this context. Therefore, when x = 6, the area of the picture equals the area of the frame. The correct answer is Choice C.
转载请注明原文地址:https://kaotiyun.com/show/F5kO777K
本试题收录于:
GRE QUANTITATIVE题库GRE分类
0
GRE QUANTITATIVE
GRE
相关试题推荐
Ifyouhavehighbloodpressure,youshould______eatingtoomuchsaltyfood.
Manyschoolteacherssaythatasdifficultastheirstudentscanbetodealwith,parentscanbeevenworse.Someparentsarequi
Lifeasawomaninthecolonial(殖民的)Americaseemsquitedifferentfromitistoday.Womenwereconsideredinferiortomen,afac
AsTheplanecircledovertheairport,everyonesensedthatsomethingwaswrong.Theplanewasmovingunsteadilythroughtheair
AsTheplanecircledovertheairport,everyonesensedthatsomethingwaswrong.Theplanewasmovingunsteadilythroughtheair
Astudyofarthistorymightbeagoodwaytolearnmoreaboutaculturethanispossibletolearningeneralhistoryclasses.M
Theunderlinedword"average"inParagraph1means______.Thebesttitleforthispassagemaybe______.
Evans:Ijustreceivedaletterfromoneofmyoldhighschoolbuddies.Danae:【D5】______Evans:Well,actuallyIhaven’t
Don’t__________thecamera____________unlessyouaresureyoucanputittogether.
Intherectangularquadrantsystemshownabove,whichquadrant,ifany,containsnopoint(x,y)thatsatisfiestheequationx2-2
随机试题
糖尿病合并中度肾功能不全时应选用的降糖药为
下列哪项提示无排卵
在常规格式下,在Excel单元格中输入3/4,则单元格中的数据为()。
下列各项中,属于检查性控制的有()。
一列火车的车身长800米,行驶的速度是每小时60千米,铁路上有两座隧洞且长度相等。火车从车头进入第一个隧洞到车尾离开第一个隧洞用2分钟,从车头进入第一个隧洞到车尾离开第二个隧洞共用6分钟。两座隧洞之间相距多少千米?()
完成全面建成小康社会和实现现代化的历史性任务,重点和难点都在()。
发生重大突发事件时,根据安全第一的原则,首先应考虑将现场人员疏散至安全区域,以免造成更大的人员伤亡。以下关于火灾安全疏散的建议,错误的是()。
A、B、C三人从法学院毕业后,一人去了律师事务所,一人去了法院,一人去了检察院。甲、乙、丙三人做了以下猜测:甲:“A去了律师事务所,B去了法院。”乙:“A去了法院,C去了律师事务所。”丙:“A去了检察院,B去了律师事务所。”如果甲、乙、丙三人的猜测都只对了
AspartofeffortstoreduceilliteracyandpromoteEducationForAll(EFA)goals,theLagosStateAgencyforMassEducationha
WhatarethetwoseasoningsusedbymostAmericans?
最新回复
(
0
)