<s>[INST] what is the no. of possible parellelograms? A parallelogram having an acute angle of 30 degrees whose area is equal to the perimeter and the sides are whole numbers then number of such parallelograms possible are?
 [/INST] We interpret the question to mean that we want to find the number of (unordered) pairs $a$, $b$ of integers that can be the sides. The perimeter is $2a+2b$. The area is twice the area of the triangle we get by joining the two vertices at which there is a $150^\circ$ angle. 
The area of each of these triangles is $(1/2)(ab)(\sin 30^\circ)$, for a total of $(1/2)ab$. So we are looking at the equation $2a+2b=(1/2)(ab)$, or equivalently $ab=4a+4b$.
This equation can be rewritten as $(a-4)(b-4)=16$.  Thus $a-4$ and $b-4$ must have product $16$. Without loss of generality we may assume that $a\le b$.
It is easy to see that $a-4$ and $b-4$ cannot both be negative. So $a-4=1$, $b-4=16$, or $a-4=2$, $b-4=8$, or $a-4=4$, $b-4=4$. 
That gives three parallelograms: one with sides $5$ and $20$; another with sides $6$ and $12$;  and finally the rhombus with sides $8$ and $8$. 
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