question_answer

Let LMNP be a parallelogram and NR be perpendicular to LP. If the area of the parallelogram is six times the area of \[\Delta \mathbf{RNP}\] and RP = 6 cm then LR is equal to

A)  15 cm                         

B)  12cm  

C)  9 cm               

D)  8 cm

Correct Answer: B

Solution :

(b): by given condition, Area of parallelogram \[=6\times area\text{ }of\text{ }\Delta NPR\] \[\therefore \]\[NR\times PL=6\times \frac{1}{2}\times NR\times pR\] \[\Rightarrow \]\[PL=3PR\]                    \[(here,PL=PR+RL)\] \[\Rightarrow \] \[PR+RL=3PR\] \[\Rightarrow \]\[RL=2PR=2\times 6=12\]cm.