The perimeter of the rectangle is 83 1/3 cm, the aspect ratio is 3: 2. 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 lengths of the sides of a given rectangle are related as 3: 2, therefore, we can write the following ratio:
x / y = 3/2.
It is also known that the perimeter of this rectangle is 83 1/3 cm.
Let’s convert the correct fraction 83 1/3 to the incorrect one:
83 1/3 = 83 + 1/3 = 249/3 + 1/3 = 250/3.
Now we can write the following ratio:
2 * (x + y) = 250/3.
We solve the resulting system of equations.
Substituting in the second equation the value x = (3/2) * y from the first equation, we get:
2 * ((3/2) * y + y) = 250/3;
2 * (5/2) * y = 250/3;
5 * y = 250/3;
y = (250/3) / 2;
y = 125/3 cm.
Knowing y, we find x:
x = (3/2) * y = (3/2) * (125/3) = 125/2 cm.
Knowing the lengths of the sides of a given rectangle, we find its area:
x * y = (125/3) * (125/2) = 15625/6 = 2604 1/6 cm².
Answer: the area of ​​this rectangle is 2604 1/6 cm².