question_answer

In ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR = 2 cm, then BC is equal to

A) 4 cm

B) 2 cm

C) 12 cm

D) 6 cm

Correct Answer: C

Solution :

[c] Since, P, S Q are the mid-points of AB and BC, therefore \[\frac{AP}{AB}=\frac{PQ}{BC}=\frac{1}{2}\]                          (i) Now,     \[\frac{PR}{RQ}=\frac{1}{2}\]\[\Rightarrow \]\[\frac{2}{RQ}=\frac{1}{2}\]\[\Rightarrow \]\[RQ=4\] \[\therefore \]      \[PQ=2+4=6\,cm\] Therefore, from Eq. (i), we get \[\frac{6}{BC}=\frac{1}{2}\]\[\Rightarrow \]\[BC=12\,cm\]