The perimeter of the rectangle is 24 point 1/3 cm, the length is 7 point 1/6. Find the area of the rectangle.

Let’s take advantage of the fact that the perimeter of a rectangle is twice the sum of the length and width of this rectangle.
Let’s denote the width of this rectangle through x. According to the condition of the problem, the perimeter of this rectangle is 24 whole 1/3 cm, and its length is 7 whole 1/6, therefore, we can write:
2 * (43/6 + x) = 73/3.
We solve the resulting equation:
2 * 43/6 + 2 * x = 73/3;
43/3 + 2 * x = 73/3;
2 * x = 73/3 – 43/3;
2 * x = 30/3;
2 * x = 10;
x = 5.
Knowing the length and width of this rectangle, we find its area S:
S = (43/6) * 5 = 215/6 = 35 5/6 sq. Cm.
Answer: the area of ​​this rectangle is 35 5/6 (35 integers and 5/6) square cm.