How do you show that it is impossible to form a 20 cm length of wire into a rectangle with area 30 cm^2?
No, it is not possible.
I would like to put things in a simpler way.
Although both the answers given by bpeacock and Nick Bland are correct, what they are saying is given a perimeter of a rectangle, it is the square which has the maximum area. As a wire of 20 cm can make a square of only 5 cm side, the maximum area that can be covered by this wire is 25 square centimeters.