The sides of the rectangle are 4: 9, and its area is 144 cm, then the larger side is equal.

Let one part be equal to X, then the length of the smaller side is 4X, and the length of the larger side is 9X.

The area of a rectangle is the product of the larger side by the smaller side. Then we compose the equation according to the known data:

4X * 9X = 144;

36X = 144;

X = 144/36;

X = 4.

To find out the length of the larger side, we multiply the value of one part by 9:

4 * 9 = 36 cm.

Answer: 36 cm.