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

Let us denote the lengths of the sides of this rectangle through x and y.
According to the condition of the problem, the perimeter of this rectangle is 66 dm, therefore, the following relation holds:
2 * (x + y) = 66.
It is also known that the length of one of the sides of this rectangle is 3/11 of the perimeter, therefore, the following relationship holds:
x = 66 * 3/11 = 6 * 3 = 18.
Substituting into the equation 2 * (x + y) = 66 the obtained value x = 18, we get:
2 * (18 + y) = 66.
We solve the resulting equation:
18 + y = 66/2;
18 + y = 33;
y = 33 – 18;
y = 15.
Find the area S of this rectangle:
S = x * y = 18 * 15 = 270 dm².
Answer: the area of ​​this rectangle is 270 dm².