The side of one square is 2 cm larger than the other, and the difference in the areas

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

1) Let x cm be the side of the larger square.

2) Then (x – 2) cm is the side of the smaller square.

3) x ^ 2 (cm ^ 2) – the area of the larger square, (x – 2) cm ^ 2 – the area of the smaller square.

4) By the condition of the problem, the difference between the areas of these squares is 24 cm ^ 2, so you can make up the equality:

x ^ 2 – (x – 2) ^ 2 = 24.

5) Let’s solve the resulting equation:

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.

6) Having solved the equation, we find that x = 7 cm is the side of the larger square.

Answer: 7 cm.