The side of one square is 2 cm less than the side of the other square, and the difference

The side of one square is 2 cm less than the side of the other square, and the difference in the areas of these squares is 24 cm². Find the side of the larger square.

Let the side of the larger square be x cm, then the side of the smaller square is (x – 2) cm. The area of the square is equal to the product of its sides S = a * a = a ^ 2. The area of the larger square is x ^ 2 cm ^ 2, and the area of the smaller square is (x – 2) ^ 2 cm ^ 2. By the condition of the problem, it is known that the difference between the areas of these squares is equal to (x ^ 2 – (x – 2) ^ 2) cm ^ 2 or 24 cm ^ 2. Let’s make an equation and solve it.
x ^ 2 – (x – 2) ^ 2 = 24;
x ^ 2 – (x ^ 2 – 4x + 4) = 24;
x ^ 2 – x ^ 2 + 4x – 4 = 24;
4x – 4 = 24;
4x = 24 + 4;
4x = 28;
x = 28: 4;
x = 7 (cm).
Answer. 7 cm.