Is it possible to bend a 20cm length of wire into a rectangle with area 30cmsquared

No.

to get an area of 30 cm squared the measurements of the rectangle would have to be something like 1x30, 2x15, 3x10, 5x6, etc. to find the perimeter of those rectangles (in other words, the length of the wire needed to complete it) you double the width and add it to double the length. for all the given suggestions, none produce a perimeter shorter than 22cm.

alternatively, you could also say 20cm must be bent so that x does not equal y when 2x+2y=20 and that xy=30. you will find that the math doesnt check out.