Answer:
p=20cm
Step-by-step explanation:
Area of parallelogram is :[tex]24cm^{2}[/tex]
Since, it is a parallelogram, the four triangles are created by drawing diagonals of equal area=[tex]\frac{24}{4}=6cm^{2}[/tex].
Now, Height of the one triangle is 2cm and the other is 3 cm.
Therefore, From ΔODC,
Area=[tex]\frac{1}{2}{\times}b_{1}{\times}h_{1}[/tex]
[tex]6[/tex]=[tex]\frac{1}{2}{\times}b_{1}{\times}2[/tex]
[tex]b_{1}=6[/tex]
[tex]DC=6cm[/tex]
Again, from ΔOAD,
Area=[tex]\frac{1}{2}{\times}b_{2}{\times}h_{2}[/tex]
[tex]6=\frac{1}{2}{\times}b_{2}{\times}3[/tex]
[tex]b_{2}=4cm[/tex]
[tex]AD=4cm[/tex]
Now, opposite sides of parallelogram are equal, therefore,AD=BC=4cm and DC=AB=6cm.
Perimeter of parallelogram= Sum of all the sides
=AB+BC+CD+AD
=6+4+6+4
=20cm
