question_answer

In a rectangle ABCD, P, Q are the mid-points of BC and AD respectively and R is any point on PQ, then \[\Delta \mathbf{ARB}\] equals:

A)  \[\frac{1}{2}\left( [\,\,\,\,]\,ABCD \right)\]

B)  \[\frac{1}{3}\left( [\,\,\,]\,ABCD \right)\]

C)  \[\frac{1}{4}\left( [\,\,\,]\,ABCD \right)\]

D)  None of these

Correct Answer: C

Solution :

(c):-  \[area([\,\,\,]\,ABPQ)=\frac{1}{2}area([\,\,\,]\,ABCD)\] and area \[\left( [\,\,\,]\,ARB \right)=\frac{1}{2}area\left( [\,\,\,]\,ABPQ \right)\] \[\therefore \]\[area\left( \Delta ARB \right)=\frac{1}{4}area\left( [\,\,\,]\,ABCD \right)\]