The area of one square is 13 cm square less than the area of another

The area of one square is 13 cm square less than the area of another. Find the perimeter of each of these squares if the sides of one are 1 cm less than the sides of the other.

1. By the statement of the problem, it is known that the sides of two squares differ by 1 cm, and their areas by 13 cm².

2. Let’s designate the side length of one square for x cm, then the value for the other (x – 1) cm.

The formula for the area of a square for the first x², for the second (x – 1) ².

Let’s make the equation

x² – (x – 1) ² = 13;

x² – x² + 2 x – 1 = 13;

2 x = 13 + 1 = 14;

x = 14: 2 = 7 cm.

The perimeter of the first square is 4 * 7 cm = 28 cm, and the second (7 – 1) cm * 4 = 6 cm * 4 = 24 cm².

Answer: The perimeters of the squares are 28 cm and 24 cm.