What should be the side of a square for its perimeter and area to coincide numerically?

1. The perimeter of a polygon is equal to the sum of the lengths of all its sides. Since all sides of a square are equal, we can denote them by one variable a. Thus, the perimeter of the square is:

P = a + a + a + a = 4 * a.

2. Since a square is a special case of a rectangle, its area is equal to the product of one side of it by the other (adjacent):

S = a * a = a².

3. By condition, the perimeter and area of the square are the same:

P = S;

4 * a = a².

Let’s solve an incomplete quadratic equation:

a² – 4 * a = 0;

a * (a – 4) = 0;

a₁ = 0;

a₂ – 4 = 0 ⇒ a₂ = 4.

Answer: a = 4.