Question

PQR is a triangle. S is a point on the side QR of ∆PQR such that ∠PSR = ∠QPR. 

Given QP = 8 cm, PR = 6 cm and SR = 3 cm. 

(i) Prove ∆PQR ~ ∆SPR 

(ii) Find the length of QR and PS

(iii) area of ΔPQR/area of ΔSPR

Answer 1

Given : QP = 8 cm, PR = 6 cm and SR = 3 cm 

In ∆PQR and ∆SPR 

∠QPR = ∠PSR (given) 

∠QRP = ∠SRP (common) 

(i) ∴ ∆PQR ~ ∆SPR (by AA similarity rule)

Since ∆PQR ~ ∆SPR

(ii) 12 cm and 4 cm 

(iii) 4/1