question_answer

Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle, thus formed, with that of the original triangle is

A) \[3:2\]                           

B) \[4:1\]

C) \[2:1\]                 

D)        \[2:3\]

Correct Answer: C

Solution :

            \[AQ||CB\], and\[AC||QB\] \[\therefore \]\[AQBC\], is a parallelogram \[\Rightarrow \]   \[BC=AQ\] Again, \[AR||BC\] and\[AB||RC\] \[\therefore \]\[ARCB\]is a parallelogram. \[\Rightarrow \]   \[BC=AR\Rightarrow AQ=AR\] \[\Rightarrow \]   \[AQ=AR=\frac{1}{2}QR\] Similarly, \[AB=\frac{1}{2}PR\] and             \[AC=\frac{1}{2}PQ\] \[\therefore \]Required ratio             \[=(PQ+QR+RP):(AB+BC+CA)\]             \[=2:1\]