Given that the area of parallelogram MNOP is 48 square units and MX= 3, find the length of the diagonal NP. Figure: http://www.flickr.com/photos/93084714@N07/8594014140/in/photostream

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In parallelogram OPMN , diagonal PN divides it into two congruence triangle OPN and NMP.

so 

   area   of triangle (OPN) = area of triangle (PMN)

Area of Triangle (PMN)=(1/2) area of parallelogram OPMN

                               =(1/2) . 48

                                 =   24

But

area of traingle (PMN)= (1/2) x 3 x PN

          24 =   (1/2) x  3 x PN

         PN = 16 unit

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