question_answer

In APQR, S and T are points on the sides PQ and PR respectively. ST is parallel to QR. If lengths of PS, SQ and PR are 6 cm, 9 cm and 12.5 cm respectively, what is the length of TR?

A)  7.5 cm

B)  5 cm

C)  10 cm

D)  2.5 cm

Correct Answer: A

Solution :

ST. || QR, \[\therefore \]\[\angle PST=\angle PQR\] \[\angle PTS=\angle PRQ\] By AA- similarity \[\Delta PST\tilde{\ }\Delta PQR\] \[\therefore \]\[\frac{PS}{SQ}=\frac{PT}{TR}=\frac{PR-TR}{TR}\] \[\Rightarrow \]\[\frac{6}{9}=\frac{125-x}{x}\]                 \[[x=TR]\] \[\Rightarrow \]\[\frac{2}{3}=\frac{125-x}{x}\] \[\Rightarrow \]\[2x=37.5-3x\] \[\Rightarrow \]\[5x=37.5\] \[\Rightarrow \]\[x=\frac{37.5}{5}=7.5\,cm\]