首页
登录
职称英语
If the lengths of two sides of a triangle are 5 and 9, respectively, which of th
If the lengths of two sides of a triangle are 5 and 9, respectively, which of th
游客
2024-01-12
37
管理
问题
If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle?
Indicate
all
such lengths.
选项
A、3
B、5
C、8
D、15
答案
B,C
解析
A good way to approach this problem is to think about how much the length of the third side of a triangle with two fixed side lengths can vary. If you think about it a bit, you will see that the smaller the interior angle between the two sides of the triangle is, the smaller the length of the third side is; and the larger the interior angle between the two sides of the triangle is, the larger the length of the third side is. This suggests drawing two triangles, one in which the angle between the two sides is close to 0 degrees and one in which the angle between the two sides is close to 180 degrees, like the triangles below.
In the triangle in which the angle between the sides of length 5 and 9 is small, you can see that the length of the third side is a bit greater than 9 - 5, or 4. If it were equal to 4, the triangle would degenerate into a line segment.
In the triangle in which the angle between the sides of length 5 and 9 is large, you can see that the length of the third side is a bit less than 9 + 5, or 14. If it were equal to 14, the triangle would degenerate into a line segment.
Therefore, the length of the third side of the triangle must be greater than 4 and less than 14. Furthermore, it is intuitive that any length between these two numbers can be achieved by some triangle. The correct answer consists of Choices B and C.
转载请注明原文地址:https://tihaiku.com/zcyy/3355858.html
相关试题推荐
Inarightisoscelestriangle,thelengthsofthetwononhypotenusesidesarede
If4and11arethelengthsoftwosidesofatriangularregion,whichofthefo
Thephysicalstructureofthehumaneyeenablesittosenselightofwavelengths
Iftheperimeterofatriangleis18,thenthelengthofoneofthesidesCANNOT
Ifasquareandanequilateraltrianglehaveequalperimeters,whatistheratio
Ifthelengthsoftwoofthesidesofatriangleare9and10,whichofthefoll
Intherighttrianglebelow,ifx=9,whatisthevalueofy?[img]2012q1/ct_egr
Whatistheareaofthetriangleinthefigurebelow?[img]2012q1/ct_egreqm_egreq
Whatisthehypotenuseofarighttrianglewithabaseof9cmandanareaof54
[img]2014m5x/ct_egreqm_egreqjs_0067_20135[/img]IntriangleABC,whatistheval
随机试题
Wherearethereligiousbelieversfrom?[br][originaltext]PoliceinCalifo
首选的preferred
Inthecauseofequalrights,feminists(女权主义者)havehadmuchtocomplainab
Somethingsarebestkeptsecret.Itishard,forinstance,toarguethatpu
Theyoungmanassuredthebossthathewould______allhisenergiestodothejo
________aresearchstudent,Iwouldatleastmastertwoforeignlanguages.A、Shou
A.产能占总热量的10%~15% B.产能占总热量的55%~70% C.产能
口渴、尿少、比重高、皮肤弹性差系A.高渗性脱水 B.低渗性脱水 C.等渗性脱
关于仲裁时效制度的特征。说法正确的是()。A.仲裁时效具有消灭时效的特征 B
巴黎圣母院大火敲响文保警钟 昨天,当很多人在早晨打开手机时,巴黎圣母院起火
最新回复
(
0
)