question_answer

In \[\Delta PQR,\] S and T are points on the sides PQ and PR respectively such that \[ST\left\| QR \right.\]. If \[\text{PS}=\text{4 cm},\] \[\text{PQ}=\text{9 cm}\] and \[\text{PR}=\text{4}\text{.5cm},\]then PT is:            (CBSE2014, 15, 16, 17)

A) 1 cm

B) 2 cm  

C) 7 cm

D) 11cm

Correct Answer: B

Solution :

 

[b] Given, \[PS=4cm,\] \[PQ=9cm\] and \[PR=4.5cm\]

Since \[ST||QR,\] then by BPT, we have

\[\frac{PS}{PQ}=\frac{PT}{PR}\,\Rightarrow \frac{4}{9}=\frac{PT}{4.5}\]

or         \[PT=\frac{4\times 4.5}{9}=2\,\,cm\]

Hence, \[PT=2\,cm\].