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Parallelogram ABCD and rectangle ABEF on same base AB have equal areas. ....Given
AB=CD ...opposite side of parallelogram
AB=EF ...opposite side of rectangle
and, ∠F=∠E=90
AD>AF and BC>BE ....(Hypotenuse of right angle is greater than other sides )
Now,
Perimeter of □ABCD=AB+BC+CD+DA
Perimeter of □ABEF=AB+BE+EF+FA
Also, CD=EF and AD>AF,BC>BE
∴ Perimeter of parallelogram ABCD> Perimeter of rectangle ABEF
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