Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If one vertex of an equilateral triangle is at (2,-1) and the base is , then th

If one vertex of an equilateral triangle is at (2,-1) and the base is \mathrm{x+y-2=0}, then the length of each side is

Option: 1

\sqrt{3 / 2}


Option: 2

\sqrt{2 / 3}


Option: 3

2 / 3


Option: 4

3 / 2


Answers (1)

best_answer

 Let \mathrm{A(2,-1) }be one vertex of an equilateral triangle \mathrm{A B C}. Then its altitude is the length of the perpendicular from \mathrm{A(2,-1)} on \mathrm{x+y-2=0} i.e.

\mathrm{A D=\left|\frac{2-1-2}{\sqrt{1+1}}\right|=\frac{1}{\sqrt{2}}}

\mathrm{\text { In } \triangle A B D, \sin 60^{\circ}=\frac{A D}{A B}}

\mathrm{\therefore \: A B=A D \operatorname{cosec} 60^{\circ}=\frac{1}{\sqrt{2}} \times \frac{2}{\sqrt{3}}=\sqrt{\frac{2}{3}}}.

Posted by

Shailly goel

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

'Why are they dying only in Kota': SC grills Rajasthan over surge in student suicides
anam-khan

JEE Main 2025 paper 2 final answer key out; NTA drops 4 questions, 2 from BPlanning
anam-khan

JEE Main 2025 session 2 answer key out for BArch, BPlanning; response sheet on jeemain.nta.nic.in

Latest Question