Find the area of a rectangle if its perimeter is 52 cm and its length is 2 cm more than its width.

1) Find the lengths of the sides of the rectangle. Let’s denote x, y – the lengths of the sides of the rectangle. Then, the perimeter of the rectangle is 2 * (x + y) = 52. Also, by the condition: x = y + 2. We got the system of equations, substitute the second equation into the first and calculate y:

2 * (y + 2 + y) = 52;

2 * (2y + 2) = 52;

4y + 4 = 52;

4y = 48;

y = 12.

x = y + 2 = 12 + 2 = 14.

2) Calculate the area of the rectangle:

S = x * y = 12 * 14 = 168.

Answer: S = 168.