A rectangle has one side 2 cm longer than the other, and the perimeter is 28. which is equal to the area of this rectangle.

Since the opposite sides of the rectangle are equal, then its perimeter is:

P = a + b + a + b = 2 * a + 2 * b,

where a is the length of the rectangle, b is the width of the rectangle.

By condition, the length of the rectangle is 2 cm longer than its width, then a = 2 + b.

Also, by condition, the perimeter is 28 cm.

Substitute the known values ​​into the perimeter formula:

2 * (2 + b) + 2 * b = 28.

Let’s solve the resulting equation with one variable:

2 * 2 + 2 * b + 2 * b = 28;

4 + 2 * b + 2 * b = 28;

Let us leave the terms with the variable on the left side of the equation, and transfer all natural terms to the right side (during the transfer, we must change the sign to the opposite):

2 * b + 2 * b = 28 – 4.

We present similar terms in both sides of the equation:

4 * b = 24;

b = 24/4 (proportional);

b = 6 cm.

Find the length:

a = 2 + b = 2 + 6 = 8 (cm).

The area of ​​a rectangle is equal to the product of its length and width, then:

S = a * b = 8 * 6 = 48 (cm²).

Answer: S = 48 cm².