In ΔPQR, S and T are point on sides PR and PQ respectively such that ∠PQR = ∠PST, If PT = 5 cm, PS = 3 cm and TQ = 3 cm, then length of SR is

A. 5 cm

B. 6 cm

C. $$\frac{{31}}{3}$$ cm

D. $$\frac{{41}}{3}$$ cm

Answer: Option C

Solution(By Examveda Team)

According to question,

Given :
PT = 5 cm
PS = 3 cm
TQ = 3 cm
SR = ?
ΔPQR ∼ ΔPST

$$\eqalign{ & \frac{{PR}}{{PT}} = \frac{{PQ}}{{PS}} \cr & \frac{{PR}}{5} = \frac{8}{3} \cr & PR = \frac{{40}}{3} \cr & \therefore SR = PR - PS \cr & SR = \frac{{40}}{3} - 3 \cr & SR = \frac{{40 - 9}}{3} \cr & SR = \frac{{31}}{3}\,{\text{cm}} \cr} $$