The length of the rectangle is 1.25 times its width. Help find its area if the perimeter of the rectangle is 66.6 centimeters.

Let’s denote the width of the rectangle through x. Then the length of the rectangle is 1.25x. It is further known that the perimeter is 66.6.
Find the sides of the rectangle. Since the perimeter is equal to the sum of all the lengths of the sides of the rectangle. We write the expression.
66.6 = (x + 1.25x) × 2.
x + 1.25x = 66.6 ÷ 2.
2.25x = 33.3.
Find the unknown value of x.
x = 33.3 ÷ 2.25 = 14.8.
This means that the width of the rectangle is 14.8.
14.8 x 1.25 = 18.5.
Next, we find the area of the rectangle.
S = a × b = 14.8 × 18.5 = 273.8.
This means that the area of the rectangle is 273.8.
Answer: S = 273.8.