The length of the rectangle is 8 cm less than the width. Find the area of the rectangle if the perimeter of the rectangle is 72 cm.

Let’s denote by x the length of the rectangle, then the width of the rectangle will be x + 8. Since we know the value of the perimeter, we can find the width and length. To do this, we substitute our data into the formula for finding the perimeter:

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

72 = (x + x + 8) * 2;

Next, we solve this equation:

72 = (2x + 8) * 2;

72 = 4x + 16;

4x = 56;

x = 56: 4;

x = 14 (cm) – length;

Now we find the width:

14 + 8 = 22 (cm) – width.

Next, we find the area of the rectangle:

S = a * b = 14 * 22 = 308 (cm²).

Answer: 308 cm².