Given that the area of parallelogram MNOP is 48 square units and MX= 3, find the length of the diagonal NP.

Figure:

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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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