The perimeter of the rectangle is 66 dm. The length of one side is 3/11 of the perimeter. Find the area of the rectangle.

In order to find the part of an integer value, you must divide it by the denominator of the fraction and multiply by its numerator.
Based on this rule, we find the length of the rectangle, provided that it is 3/11 of its perimeter, equal to 66 dm:

66: 11 * 3 = 18 dm.

The sum of all sides of such a figure corresponds to the formula:
P = 2a + 2b.

Substituting the known values, write the equation:

2 * 18 + 2b = 66.

We transfer the known number to the right side of the equation, while changing the sign in front of it to the opposite.

2b = 66 – 36 = 30.

b = 30: 2 = 15 dm.

The area corresponds to:
S = a * b = 18 * 15 = 270 dm².