Find the sides of a rectangle whose perimeter is numerically equal to the area and the sides are natural numbers.

By condition, P = S, S is the area of the rectangle, P is the perimeter of the rectangle.

Hence,

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

2 * a / (a * b) + 2 * b / (a * b) = 1.

1 / b + 1 / a = ½.

1 / b = ½ – 1 / a = (a – 2) / (2 * a).

From the last equality, note that in order for the length of the side b to be a natural number, it is necessary that the difference (a – 2) = 1.

Hence, side a = 3.

Then, 1 / b = (3 – 2) / (2 * 3) = 1/6.

b = 6.

Let’s check:

2 * (3 + 6) = 3 * 6.

18 = 18.

Answer: The sides of the rectangle are 3 and 6.