Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

In triangle PQR, p,q,r in G.P. and p^2,q^2,r^2 \ are\ in\ A.P. then which of the following is true about triangle PQR

Option: 1

Triangle\ PQR \ is\ a\ scalene\ triangle


Option: 2

Triangle\ PQR \ is\ a\ isosceles \ triangle


Option: 3

Triangle\ PQR \ is\ a\ equilateral\ triangle


Option: 4

Can't say anything 


Answers (1)

best_answer

Basic relation b/w sides and angle of triangle and Sine Rule -

Basic relation b/w sides and angle of triangle and Sine Rule

 

In this section, Properties and solution of Triangle. We will be using some standard symbols.

 In ΔABC, the angles are denoted by capital letters A, B and C and the length of the sides opposite to these angles are denoted by small letters a, b and c respectively.

 

\mathrm{\begin{array}{l}{ \angle B A C=A} \\ { \angle A B C=B} \\ { \angle B C A=C}\end{array}}

 

Sides of the ΔABC

AB = c, AC = b, and  BC = a

Collectively, these relationships are called the Law of Sines

 

\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}

-

 

p,q,r \ in\ G.P. \rightarrow q^2=pr\\ p^2,q^2,r^2 \ are\ in\ A.P.\rightarrow 2q^2=p^2+r^2\\ 2pr=p^2+r^2\\ (p-r)^2=0\\ p=r\\ \because q^2=pr\\ p=q=r\\ Triangle\ PQR \ is\ a\ equilateral\ trianglep,q,r \ in\ G.P. \rightarrow q^2=pr\\ p^2,q^2,r^2 \ are\ in\ A.P.\rightarrow 2q^2=p^2+r^2\\ 2pr=p^2+r^2\\ (p-r)^2=0\\ p=r\\ \because q^2=pr\\ p=q=r\\ Triangle\ PQR \ is\ a\ equilateral\ triangle

Posted by

vinayak

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions