首页
登录
职称英语
[img]2014m9x/ct_egreqm_egreqtbz1_0026_20148[/img]Which of the following stateme
[img]2014m9x/ct_egreqm_egreqtbz1_0026_20148[/img]Which of the following stateme
游客
2024-01-12
70
管理
问题
Which of the following statements
individually
provide(s)sufficient additional information to determine the area of triangle ABC above? Indicate
all
such statements.
选项
A、DBC is an equilateral triangle.
B、ABD is an isosceles triangle.
C、The length of BC is equal to the length of AD.
D、The length of BC is 10.
E、The length of AD is 10.
答案
A,D
解析
From the figure you know that ABC is a right triangle with its right angle at vertex B. You also know that point D is on the hypotenuse AC. You are given that the length of AB is 10
. However, because the figure is not necessarily drawn to scale, you don’t know the lengths of AD, DC, and BC. In particular, you don’t know where D is on AC.
The area of a triangle is 1/2(base)(height). Thus, the area of right triangle ABC is equal to 1/2 of the length of AB times the length of BC. You already know that the length of AB is 10
. Any additional information that would allow you to calculate the length of BC would be sufficient to find the area of triangle ABC. You need to consider each of the five statements individually, as follows.
Statement A: DBC is an equilateral triangle. This statement implies that angle DCB is a 60° angle; and therefore, triangle ABC is a 30°-60°-90° triangle. Thus the length of BC can be determined, and this statement provides sufficient additional information to determine the area of triangle ABC.
Statement B: ABD is an isosceles triangle. There is more than one way in which triangle ABD can be isosceles. Below are two redrawn figures showing triangle ABD as isosceles. In the figure on the left, the length of AD is equal to the length of DB; and in the figure on the right, the length of AB is equal to the length of AD.
Either of the figures could have been drawn with the length of BC even longer. So, statement B does not provide sufficient additional information to determine the area of triangle ABC.
Statement C: The length of BC is equal to the length of AD. You have no way of finding the length of AD without making other assumptions, so statement C does not provide sufficient additional information to determine the area of triangle ABC.
Statement D: The length of BC is 10. The length of BC is known, so the area of triangle ABC can be found. Statement D provides sufficient additional information to determine the area of triangle ABC.
Statement E: The length of AD is 10. The relationship between AD and BC is not known, so statement E does not provide sufficient additional information to determine the area of triangle ABC.
Statements A and D individually provide sufficient additional information to determine the area of triangle ABC. Therefore, the correct answer consists of Choices A and D.
转载请注明原文地址:https://tihaiku.com/zcyy/3355761.html
相关试题推荐
Allthefollowingcasesareon-the-jobsmokingexceptthat______.[br]According
Inmakingmarketinvestigation,oneshould______.[br]Allthefollowingarech
Inmakingmarketinvestigation,oneshould______.[br]Whichofthefollowings
Acupunctureis______.[br]Whichstatementisnottrueoftheperformerofacup
In1863,AbrahamLincolnwas______.[br]WhichofthefollowingstatementsisN
Whichofthefollowingcanbeinferredfromthepassage?[br]Thebestconclusio
Whichofthefollowingcanbeinferredfromthepassage?[br]Thedifferencebet
Whichofthefollowingcanbeinferredfromthepassage?[br]Accordingtothea
WhiletakingataxiinFinland,______.[br]WhichofthefollowingisNOTtrue
Thefirstuseofumbrellawasas______.[br]Whichofthefollowingmaybethe
随机试题
Theexperiment,()willsoonbeannounced,wasdonebymycolleagues.A、whoseres
What,exactly,ispepperoni?Itisanair-dried【B1】______sausagewithafew
下面的广域网络中属于电路交换网络的是()。A.ADSL B.X.25 C
直接剪切试验是测定土的抗剪强度指标值的一种方法,根据《公路土工试验规程》(JTG
教师突然中断讲课,引起分心学生的注意。这种注意是( )。A.有意注意 B.
技术分析的三项假定不包括( )。A.市场行为涵盖一切信息 B.股价具有趋势性
我国目前推荐的临床常规测定血浆葡萄糖的方法是A.邻甲苯胺法B.福林-吴法C.葡萄
对顾客体验加以管理的先决条件是( )。A.分析顾客的体验世界 B.设计品牌体
在培训方法中,( )适用于从事具体岗位所应具备的能力、技能和管理实务类的培训。
下列哪一项不属于经皮给药制剂的优点A.可避免口服给药可能发生的肝首过效应及胃肠灭
最新回复
(
0
)