Find the perimeter of the rectangle, one side of which is 3 cm smaller than the other, and the diagonal is 15 cm.

1. Let’s denote the large side of the rectangle as x cm, then the smaller side is equal to (x – 3) cm.

2. In a triangle formed by two sides and a diagonal, by the Pythagorean theorem, we calculate x, if by the condition of the problem the diagonal is 15 cm.

x ^ 2 + (x – 3) ^ 2 = 15 ^ 2;

x ^ 2 + x ^ 2 – 6 * x + 3 ^ 2 = 225;

2 x ^ 2 – 6 x + 9 = 225;

2 x ^ 2 – 6 x – 216 = 0;

x = {6 + (36 + 4 * 216 * 2) ^ 1/2}: 4;

x = (6 + 1728 ^ 1/2): 4 = (6 + 42): 4 = 12 cm.

3. Find the smaller side of the rectangle.

x – 3 = 12 – 3 = 9 cm.

4. Calculate the perimeter P.

P = 2 * 12 + 2 * 9 = 42 cm.

Answer: The perimeter is 42 centimeters.