a rectangle has a perimeter of 22cm and an area of 30 cubic meter. what are its dimensions?

area is measured in square metres, not cubic metres.

If that is what you meant ....

length ---x
width ---y
2x + 2y = 22
x+y = 11 ---> y = 11-x

xy = 30
x(11-x) = 30
11x - x^2 - 30 = 0
x^2 - 11x + 30 = 0

solve for x, it factors very nicely.