The sides of the rectangle are 2 to 6, and its perimeter is 32cm, find the area of this rectangle.

Let’s solve the problem using the equation.
1) Let x centimeters be one part, then one of the sides of the rectangle is 2 * x centimeters, and the other – 6 * x centimeters. We know that the perimeter of the rectangle is 32 centimeters. Let’s make the equation:
2 * (2 * x + 6 * x) = 32;
2 * 2 * x + 2 * 6 * x = 32;
4 * x + 12 * x = 32;
x * (4 + 12) = 32;
x * 16 = 32;
x = 32: 16;
x = 2 centimeters – one part;
2 * 2 = 4 centimeters – the length of one side of the rectangle;
6 * 2 = 12 centimeters – the length of the second side of the rectangle;
2) 4 * 12 = 48 square centimeters – the area of a rectangle.
Answer: 48 square centimeters.