Q. 7 F5.0( 1 Vote )

The lengths of the sides, , of ΔABC are in the ratio 3 : 4 : 5. Correspondence ABC PQR is similarity. If PR = 12, the perimeter of ΔPQR is ……….
A. 12

B. 36

C. 24

D. 27

Answer :

Given: In ∆ABC,


BC:CA:AB = 3:4:5


From ∆ABC and ∆PQR, the correspondence ABC PQR is similarity.


In ∆PQR,


PR = 12


To find: Perimeter of ∆PQR = ?


In ∆ABC, since we have BC:CA:AB = 3:4:5


Let the lengths of BC, CA and AB be 3t, 4t and 5t respectively. (where, t > 0)


Perimeter of ∆ABC = 3t + 4t + 5t


Perimeter of ∆ABC = 12t, t > 0


Also, from given we have,


In ∆ABC and ∆PQR, the correspondence ABC PQR is similarity.


So, from property we can say that,


Ratio of perimeters of ∆ABC and ∆PQR = Ratio of their corresponding sides



Substituting the given values, we get




Perimeter of ∆PQR = 36


Thus, option (b) is correct.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
Champ Quiz | Thales Theorem49 mins
Quiz | Criterion of Similarity of Triangle45 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
How to Ace Maths in NTSE 2020?36 mins
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :