If parallelogram ABCD and rectangle ABEM are of equal area, then:
Perimeter of AMEB Perimeter of ADCB
AD2 = AM2 + MD2 (by Pythagoras theorem)
⇒AD>AM
Similarly, BC2 = BE2 + EC2
⇒BC>BE
AB = DC = ME (opposite sides of rectangle and parallelogram)
Perimeter of rectangle = AM + ME + EB + AB.
Perimeter of parallelogram = AB + BC + DC + AD.
Hence Perimeter of ADCB > Perimeter of AMEB.