The perimeter of the rectangle is 30 cm and the area is 54 which are equal to the sides of the rectangle.

Suppose the sides of the rectangle are x and y.

Then we can write the condition of the problem in the form of two equations:

2 * (x + y) = 30,

x * y = 54.

From the first equation we get:

x + y = 15,

y = 15 – x.

Substitute this value for y in the second equation:

x * (15 – x) = 54,

-x² + 15 * x – 54 = 0.

The discriminant of this equation is:

15² – 4 * (-1) * (-54) = 9.

So this equation has the following roots:

x = (-15 – 3) / – 2 = 9 and x = (-15 + 3) / – 2 = 6.

So y has the following meanings:

y = 54: 9 = 6 and y = 54: 6 = 9.

Answer: x = 9, y = 6 or x = 6, y = 9.