SSC
Quantitative Aptitude
Geometry
Question Bank
Triangles and Their Properties (II)
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 \[\frac{6}{BC}=\frac{1}{2}\]\[\Rightarrow \]\[BC=12\,cm\]