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
44
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
Withthedevelopmentofeconomy,moreandmorepeoplewanttohavetheirown
ANewApproachtoDebateI.Teachers’hesitation:debateis
Sheisso______thatshewon’tletanyonehelpherwhensheisinsuchadilemm
[originaltext]Asinglecigarettesoldonastreetcornermaynotcostalot
A.肾小球滤过率20~50ml/min,血肌酐<442μmol/L B.肾小球
Doesyourhometownhaveanunofficialna
据2006年4月6日《新闻晚报》报道,3月份人民币汇率双向波动加剧,上周人民币汇
给定的图形是纸盒的外边面展开图,下列四个选项是由其折叠的是( ) A.如上图
中商华联贸易有限公司(海关注册编码1102918123)代理湖南长沙家佳纺织有
(2021年真题)某壁厚30mm高压钢管焊接,需加工坡口,宜选用坡口形式为( )
最新回复
(
0
)