One side of the rectangle is 11 times smaller than the other. Find the sides of a rectangle if its perimeter is 144 cm.

Let us denote by x the smaller side of this rectangle, and by y – the larger side of this rectangle.
According to the condition of the problem, one of the sides of a given rectangle is 11 times smaller than the other, therefore, the following relation holds:
y = 11 * x.
It is also known that the perimeter of this rectangle is 144 cm, therefore, the following relationship holds:
2 * (x + y) = 144.
We solve the resulting system of equations. Substituting into the second equation the value y = 11 * x from the first equation, we get:
2 * (x + 11 * x) = 144.
We solve the resulting equation:
2 * 12 * x = 144;
24 * x = 144;
x = 144/24;
x = 6.
Knowing x, we find y:
y = 11 * x = 11 * 6 = 66.

Answer: the sides of this rectangle are 6 cm and 66 cm.