The lengths of the sides of the rectangle are 3 to 6, and the perimeter is 54cm. Find the area of the rectangle.

Let’s solve the problem using the equation.
1) Let one part be x centimeters. Then one of the sides is 3 * x centimeters, and the other side is 6 * x centimeters. We know that the perimeter of the rectangle is 54 centimeters. Let’s make the equation:
2 * (3 * x + 6 * x) = 54;
3 * x + 6 * x = 54: 2;
3 * x + 6 * x = 27;
x * (3 + 6) = 27;
x * 9 = 27;
x = 27: 9;
x = 3 centimeters;
2) 3 * 3 = 9 centimeters – the length of the first side;
3) 3 * 6 = 18 centimeters – the length of the second side.
Answer: 9 and 18 centimeters.