The length of the rectangle is 20% less than its width. Find the area of a rectangle if its perimeter is 72 cm.

Let’s designate the width of the rectangle as x, then the length of the rectangle will be 0.8x. We know the perimeter of the rectangle, so we can find the length and width. To do this, we substitute the data into the formula:

P = (a + b) * 2, where P is the perimeter and a and b are the sides of the rectangle.

72 = (x + 0.8x) * 2;

we solve this equation:

72 = 1.8x * 2;

72 = 3.6x;

x = 72: 3.6;

x = 20 (cm) – width.

Find the length:

20 * 0.8 = 16 (cm) – length.

Now we can find the area of the rectangle:

S = a * b = 20 * 16 = 320 (cm²).

Answer: the area of the rectangle is 320 cm².