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

We need to find the area of the rectangle. For this we can use the formula:
S = a * b
Where
a is the length of the rectangle;
b is the width of the rectangle.
Let the length of the rectangle be denoted as a = x. Then, according to the condition, the width is b = 1.25 * x.
We know that the perimeter of a rectangle is calculated by the formula:
P = 2 * (a + b)
and is equal to P = 66.6 cm.
Then we get:
2 * (x + 1.25 * x) = 66.6;
2 * x + 2.5 * x = 66.6;
4.5 * x = 66.6;
x = 66.6 / 4.5;
x = 14.8.
That is, the length of the rectangle:
a = x = 14.8 cm.
Width:
b = 1.25 * x = 1.25 * 14.8 = 18.5 cm.
Hence the area:
S = a * b = 14.8 * 18.5 = 273.8 cm. Sq.