| In \[\Delta PQR\], \[ST||QR\], \[\frac{PS}{SQ}=\frac{3}{5}\] and \[PR=28\,cm\], then the value of PT is |
 |
A) 9.5cm
B) 9cm
C) 10cm
D) 10.5cm
Correct Answer: D
Solution :
| Given, \[ST\,|\,\,|\,QR\], \[PS/SQ=3/5\] and \[PR=28\,cm\] |
| By using basic proportionality theorem, we get |
| \[\frac{PS}{SQ}=\frac{PT}{TR}\Rightarrow \,\,\frac{PS}{SQ}=\frac{PT}{PR-PT}\] |
| \[\Rightarrow \,\,\,\frac{3}{5}=\frac{PT}{28-PT}\] |
| \[\Rightarrow \,\,\,3\left( 28-PT \right)=5PT\] |
| \[\Rightarrow \,\,\,84=5\,\,PT+3\,PT\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,PT=\frac{84}{8}\] |
| \[\Rightarrow \,\,\,\,PT=10.5\,\,\,cm\] |
| Hence, the length of PT is 10.5 cm. |
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